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Use the shell method to set up, but do not evaluate, an integral representing the volume of the solid generated by revolving the region bounded by the graphs of y=x^2 and y=4x-x^2 about the line x=6. I had the shell

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  1. Calculus

    Use the shell method to set up, but do not evaluate, an integral representing the volume of the solid generated by revolving the region bounded by the graphs of y=x^2 and y=4x-x^2 about the line x=6. I had the shell radius as (6-x) and the shell height as
  2. Math (Calculus)

    Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. y=4-x^2, y=0
  3. calculus

    Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. y = 6x y = 18 x = 0
  4. calculus

    Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis: Y=sqrt(x+2), y=x,y=4
  5. calclus

    Set up, but do not evaluate, a definite integral representing the volume of the solid formed by revolving the region of the plane bounded by the curves y = e x , x = 0 and y = e about the line x = 1 using the disk/washer method.
  6. calculus

    2. Let R be the region in the first quadrant bounded by the graphs of (x^2/9)+(y^2/81)=1 and 3x+y=9 . a. Set up but do not evaluate an integral representing the area of R. Express the integrand as a function of a single variable. b. Set up but do not
  7. calculus

    2. Let R be the region in the first quadrant bounded by the graphs of (x^2/9)+(y^2/81)=1 and 3x+y=9 . a. Set up but do not evaluate an integral representing the area of R. Express the integrand as a function of a single variable. b. Set up but do not
  8. Math

    Let A denote the portion of the curve y = sqrt(x) that is between the lines x = 1 and x = 4. 1) Set up, don't evaluate, 2 integrals, one in the variable x and one in the variable y, for the length of A. My Work: for x: integral[4,1] sqrt(1+(dy/dx)^2) dy/dx
  9. calculus

    using the method of shells, set up, but don't evaluate the integral, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Y=e^x, x=0, y=2, about y=1
  10. Calculus

    Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y = 0.5x^2 and y = x about the line x = 7. I have to use the volume by disks method, but I'm confused about how to set it up and
  11. calculus

    1.Evaluate the integral. (Use C for the constant of integration.) integral ln(sqrtx)dx 2. Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the curves about the given axis. y = 4ex, y = 4e−x, x = 1;
  12. Calculus

    Use the Shell Method to compute the volume V of the solid obtained by rotating the region enclosed by the graphs of the functions y = x^2, y = 8 − x^2,and x = 1/2 about the y-axis. Here is how I set up the integral: 2 pi integral sign [-2,2] (1/2 -
  13. Calculus - Volume By Integration

    Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the y-axis: y=(x-2)^3-2, x=0, y=25 Solve by either the disk or washer method. I calculated the volume using the shell method and got 1250pi. However,
  14. Cal 2

    Consider the region R bounded by f(x) = ln x, x = e, and the x-axis. The units on the axes are in meters. Set up, but do not evaluate, an integral representing the volume of the solid when R is rotated about the x-axis. Include units.
  15. calculus

    8). Part 1 of 2: In the solid the base is a circle x^2+y^2=16 and the cross-section perpendicular to the y-axis is a square. Set up a definite integral expressing the volume of the solid. Answer choices: integral from -4 to 4 of 4(16-y^2)dy, integral from
  16. Math

    Hi, I have to do a project on the Shell Method in my Geometry class. I have been trying to find information on that topic, but have no luck... can someone point me to the right direction as of what keyword to search for, or is there any sites or books or
  17. Calculus check

    The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-2x. Let R be the region bounded by the x-axis and the graphs of f and g. A. Find the area of R. B. The region R from x=0 to x=4 is rotated about the line x=4. Write, but do not evaluate, an
  18. calculus

    A question on my math homework that I can't seem to solve... Rotate the region bounded by y=x^2-3x and the x-axis about the line x=4. Set up the integral to find the volume of the solid. I'm pretty sure that the integral is in terms of (dy), and has bounds
  19. Calculus

    Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = -3 I got the integral from 1 to 2.718 of pi(1)^2-pi(ln(x))^2 Is this correct or is there a
  20. calc

    how do you start this problem: integral of xe^(-2x) There are two ways: 1) Integration by parts. 2) Differentiation w.r.t. a suitably chosen parameter. Lets do 1) first. This is the "standard method", but it is often more tedious than 2) You first write
  21. Calculus AP - Volume of Revolution

    Hi. I have a few calculus problems that I have to do using the washers and shell method to find out what the volume of the graph rotated is. I'll post one question at a time with my work. The problem is, I should be getting the same answer for the problem
  22. Calculus II/III

    A. Find the integral of the following function. Integral of (x√(x+1)) dx. B. Set up and evaluate the integral of (2√x) for the area of the surface generated by revolving the curve about the x-axis from 4 to 9. For part B of our question , the surface
  23. calculus

    a) Let f(z) = z^2 and γ(t) = 1 + it^3, t ∈ [0,1]. i) Write out the contour integral ∫γ f(z)dz as an integral with respect to t. You do not need to evaluate this integral. ii) Evaluate the integral ∫0,1+i z^2dz iii) What is the relationship between
  24. Math

    Let R be the region bounded by the following curves. Use the disk​ (washer) method to find the volume of the solid generated when R is revolved about the​ y-axis. y=x, y=3x, y=6 Set up the integral that gives the volume of the solid. Use increasing
  25. Calc

    Evaluate the integral using any method: (Integral)sec^3x/tanx dx I started it out and got secx(1tan^2x)/tanx. I know I just have to continue simplifying and finding the integral, but I'm stuck on the next couple of steps. Also, I have another question
  26. calculus

    the region bounded by the graph f(x)=x(2-x) and the x axis is revolved about the y axis. Find the volume of the solid. I did the integral using the shell method, but the answer wasn't correct.
  27. Calculus

    Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 2, and x = 1 is revolved around the line y = −2.
  28. calculus

    Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = −3.
  29. Calculus

    Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = −3.
  30. Calculus

    What is the best method to evaluate the integral of 1/(4x^2-9) dx a) Integration by parts b) Rewrite the integral using long division c) Rewrite the integral using partial fractions d) Use a substitution -----> my answer Can you check for me, please
  31. Math/Calculus

    How would I integrate the following by parts: Integral of: (x^2)(sin (ax))dx, where a is any constant. Just like you did x^2 exp(x) below. Also partial integration is not the easiest way to do this integral. You can also use this method. Evaluate first:
  32. Calculus

    Let A denote the portion of the curve y = sqrt(x) that is between the lines x = 1 and x = 4. 1) Set up, don't evaluate, 2 integrals, one in the variable x and one in the variable y, for the length of A. My Work: for x: ∫[4,1] sqrt(1+(dy/dx)^2) dy/dx =
  33. Calculus II

    Evaluate the integral using method of integration by parts: (integral sign)(e^(2x))sin(5x)dx
  34. Calculus Please Check my answer

    Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = -1. ANSWER: v = ∫[1,e] π(4-(lnx+1)^2) dx
  35. Calculus

    Find the volume of the solid obtained by rotating the region bounded by y=x^2, y=sqrt(x), about y=1. I have to use either the disk or washer method and i believe i use washer. i set up the integral to be pi[(1-x^3)^2 -(1-sqrt(x))^2] from 0 to 1 for my
  36. calculus

    Set up the integral that would be used to find the volume of the solid obtained by rotating the region bounded by y=x^3 , y=8, and x=0 about the x=-4. use disk/washer method.
  37. Numerical method - numerical integration

    Evaluate the following integration: I(f) = integral sign from 0 to 20 of e^(-x) dx 1. Analytically 2. Rectangle method with h= 10,5,4,2,1. 3. Mid-point method with h= 10,5,4,2,1. 4. Trapezoidal method with h= 10,5,4,2,1. 5. Simpson's method with h=
  38. Numerical method - numerical integration

    Evaluate the following integration: I(f) = integral sign from 0 to 20 of e^(-x) dx 1. Analytically 2. Rectangle method with h= 10,5,4,2,1. 3. Mid-point method with h= 10,5,4,2,1. 4. Trapezoidal method with h= 10,5,4,2,1. 5. Simpson's method with h=
  39. Calculus

    1. Express the given integral as the limit of a Riemann sum but do not evaluate: integral[0 to 3]((x^3 - 6x)dx) 2.Use the Fundamental Theorem to evaluate integral[0 to 3]((x^3 - 6x)dx).(Your answer must include the antiderivative.)
  40. Calculus

    Set up a definite integral (but do not evaluate it!) for the area of the surface obtained by rotating the curve y =x^3/3 , 0 ≤ x ≤ 1, about the x-axis. The integral should contain only one variable (x or y).
  41. Calculus

    Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if it is convergent or divergent). I know how to find the indefinite integral of csc(x) dx, but I do not know how to evaluate the improper integral.
  42. AP Calculus AB

    Set up, but do not evaluate, the integral which gives the volume when the region bounded by the curves y = Ln(x), y = 1, and x = 1 is revolved around the line y = -1. I don't understand the washer thickness topic which is why im having trouble with this
  43. calc asap!

    can you help me get started on this integral by parts? 4 S sqrt(t) ln(t) dt 1 please help! thanks! Integral t^(1/2)Ln(t)dt = 2/3 t^(3/2)Ln(t)- 2/3 Integral t^(1/2) dt = 2/3 t^(3/2)Ln(t) - 4/9 t^(3/2) Simpler method: Integral t^(a)dt = t^(a+1)/(a+1)
  44. Urgent Math

    Suppose the area under y = -x^2+1 between x = 0 and x = 1 is rotated around the x-axis. Find the volume by using Disk method and shell method.
  45. calc

    find the volume of the solid generated by revolving around the x-axis: y=e^(x-8), y=0, x=0, x=10 So I know you can use the washer method, but the shell method can also be used and it should be better. The issue is I'm not certain how to actually do it. Any
  46. math

    use the method of cylindrical shells to find the volume generated by rotation the region bounded by x=y^2+1, x=2, about y=-2. Sketch the region, the solid, and a typical shell. I know that for shells, its 2pix*f(x)*dx. i am having trouble figuring out what
  47. Calculus - Volume by Integration

    Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the y-axis: y=(x-2)^3-2, x=0, y=25 (a)solve by either the disk or washer method (b)solve by the shell method (c)state which method is easiest to
  48. calc 3

    1. Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 36x^2+25y^2=1. L= double integral R (4sin(144x^2+100y^2) dA. 2. Use the given transformation to evaluate the
  49. calculus

    Find the volume generated by revolving the region bounded by x=1, y= e^x/2, y= e^x about the x-axis? Using the washer method or would it be the shell method. I'm having trouble finding that the boundaries would be? Thank you.
  50. Calculus

    Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y= 2e^(−x), y= 2, x= 6; about y = 4. How exactly do you set up the integral? I know that I am supposed to use the washer method but I
  51. Calculus II: Shell Method for finding volumes

    Question: What is the volume of the revolution bounded by the curves of y=4-x^2 , y=x, and x=0 and is revolved about the vertical axis. First, I had found the points of intersection to get the limits and I got -2.5616 and 1.5616. And then I plug it in the
  52. ap calculus

    Find the volume if the region enclosing y=1+ sqrerootof x, x=0, y=0, and x=9 is rotated about the x axis. I used the disk method and came up with the integral: pi integral (from 0-9) of (1+sqrerootx)^2 dx, but my answer was wrong.
  53. Calculus

    Let R be the region in the first quadrant enclosed by the graph of f(x) = sqrt cosx, the graph of g(x) = e^x, and the vertical line pi/2, as shown in the figure above. (a) Write. but do not evaluate, an integral expression that gives the area of R. (b)
  54. calculus

    Find the volume V of the solid in the rst octant bounded by y = 0, z = 0, y = 3, z = x, and z + x = 4. The best part about this problem is that I solved it using basic geometry but am expected to do it using a triple integral that will take up a whole
  55. calculus

    Evaluate the integral S x/(sqrt(3x-1))dx Use U-Substitution method.
  56. Calculus

    Evaluate using tabular method: integral e^(2x)cos3xdx
  57. Calculus (math)

    The volume of the solid obtained by rotating the region enclosed by y=1/x4,y=0,x=1,x=6 about the line x=−2 can be computed using the method of cylindrical shells via an integral. it would be great if you can just even give me the function inside that I
  58. calculus please help

    what is the integral of x/(1+x^2)^2 dx This is a question of a past AP exam of calculus BC i know i have to use the substitution method where u=(1+x^2), du=2xdx. I have to find the integral but i'm just focused on the coefficient because i get a different
  59. calculus review please help!

    1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate, the integral which gives
  60. Math (Definite Integrals)

    Sketch the region given by the definite integral. Use geometric shapes and formulas to evaluate the integral (a > 0, r > 0). r ∫ sqrt(r^2 - x^2) dx -r While I recognize that this looks similar to a circle function, I'm not sure how to graph and evaluate
  61. Calculus

    Hello. I would appreciate it if someone could check my answers. I'm sorry it is so long. 1.) Let R denote the region between the curves y=x^-1 and y=x^-2 over the interval 1
  62. Math - Calculus

    Find the volume of the solid given by rotating the region bounded by the curves y=x^2, x=1, x=2, and y=0 around the y-axis a) Use the shell method b) Use the washer method. Be careful with the radius of the washer at different y.
  63. Business Calculus

    Evaluate each indefinite integral. Use the substitution method. X square root (x+3) dx
  64. Math

    Evaluate the integral of (sin 2x)/(1+cos^2 x) 1. u=cosx and du=-sinx *dx 2. evaluate the integral of -1/(1+u^2)*du 3. result is -ln(1+u^2)+C Where did the sin2x dissapear too???
  65. calc

    i need to find the definite integral from 0 to 2|b| of .... x divided by sqrt(x^2 + b^2) dx im having a lot of trouble, thanks in advance Let u = x^2 + b^2 du = 2x dx The integrand becomes (1/2) u^(-1/2) du and the integral of this is u^(1/2) = sqrt(x^2 +
  66. Calculus

    Find the volume using the shell method - about the x-axis x=y^2/3
  67. Physics

    A thin spherical shell of silver has an inner radius of 8.74 x 10-2 m when the temperature is 29.4 °C. The shell is heated to 145 °C. Find the change in the interior volume of the shell.
  68. physics

    A thin spherical shell of silver has an inner radius of 5.58 x 10-2 m when the temperature is 25.7 °C. The shell is heated to 133 °C. Find the change in the interior volume of the shell.
  69. Calculus Help

    Set up an integral for the volume a solid torus (the donut-shaped solid shown in the figure) with radii br and aR. (Let a = 6 and b = 4.) By interpreting the integral as an area, find the volume V of the torus.
  70. cal

    Consider the following. (a) Set up an integral for the volume a solid torus (the donut-shaped solid shown in the figure) with radii br and aR. (Let a = 8 and b = 2.) dy (b) By interpreting the integral as an area, find the volume V of the torus. V =
  71. Calculus AP

    Let R be the region in the first quadrant bounded by the graph y=3-√x the horizontal line y=1, and the y-axis as shown in the figure to the right. Please show all work. 1. Find the area of R 2. Write but do not evaluate, an integral expression that gives
  72. Math

    Evaluate the following definite Integral ∫x * ln(x) dx from 1 to e^(2) I used the DI method which gave me D I + ln(x) x - 1/x (x^2)/2 = (ln(x)*x^(2))/2 - ∫ 1/x * x^(2)/2 = (ln(x)*x^(2))/2 - ∫ x/2 = (ln(x)*x^(2))/2 - x^(2)/4 + C (ln(x)*x^(2))/2 -
  73. Calculus

    Hello, I have some calculus homework that I can't seem to get started..at least not on the right track? I have 3 questions 1. integral of [(p^5)*(lnp)dp] I'm using the uv-integral v du formula So first, I'm finding u and I think it's lnp.......so du is 1/p
  74. Physics

    1.71 kg of glass (ρ = 2.66 x 10^3 kg/m3) is shaped into a hollow spherical shell that just barely floats in water. What are the (a) outer and (b) inner radii of the shell? Do not assume the shell is thin. Volume = 2.66 * 10^3/1.71 V=1555.56 m^3 V=pi(r^2)h
  75. please help calculus

    find the volume of the solid formed by revolving the region bounded by y=e^x, y=0, x=o and x=1 about the y axis by using the shell method, i got v=2*pi int(o to 1) (x)(e^x) dx and my teacher said the answer is e/2 but i keep getting a different answer Are
  76. homework

    Set up a integral and evaluate it. y=x^8/9, y=1 and x=0 about the y-axis
  77. math

    integrals evaluate the definite integral from 1 to 9 of ((x-1) / (sqrt x)) dx ? Would this one be a u sub? evaluate the integral from 0 to 10 of abs value (x-5) dx? I think this one would be split but not sure how or why?
  78. Ap Calculus

    Find the following volumes formed by rotating the region bounded by: y=x^2, x^2+y^2=-2 (set up using shell method)
  79. calculus

    consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value of the integral as
  80. calculus

    consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value of the integral as
  81. Calculus

    Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if it is convergent or divergent). I know how to find the indefinite integral of csc(x) dx, but I do not know how to evaluate the improper integral, at the following particular step. I know
  82. calc check: curve length

    Find the length of the curve y=(1/(x^2)) from ( 1, 1 ) to ( 2, 1/4 ) [set up the problem only, don't integrate/evaluate] this is what i did.. let me know asap if i did it right.. y = (1/(x^2)) dy/dx = (-2/(x^3)) L = integral from a to b for:
  83. Calculus

    Find the volume of the solid whose base is the region in the xy-plane bounded by the given curves and whose cross-sections perpendicular to the x-axis are (a) squares, (b) semicircles, and (c) equilateral triangles. for y=x^2, x=0, and y=0 (a) integral
  84. Calculus

    integral -oo, oo [(2x)/(x^2+1)^2] dx (a) state why the integral is improper or involves improper integral *infinite limit of integration (b) determine whether the integral converges or diverges converges? (c) evaluate the integral if it converges I know
  85. calculus

    The volume of the solid obtained by rotating the region enclosed by y=x^2 y=2x about the line x=2 can be computed using the method of disks or washers via an integral The volume is V
  86. calulus

    The volume of the solid obtained by rotating the region enclosed by y=x^2 y=2x about the line x=2 can be computed using the method of disks or washers via an integral The volume is V
  87. calculus

    The volume of the solid obtained by rotating the region enclosed by y=x^2 y=2x about the line x=2 can be computed using the method of disks or washers via an integral The volume is V
  88. calculus

    The volume of the solid obtained by rotating the region enclosed by y=1/x^4 y=0 x=2 x=4 about the line x=−5 can be computed the method of cylindrical shells via an integral The volume is V
  89. Math

    1. Evaluate the indefinite integral ([6x^2 + 12x^(3/2) +4x+9]/sqrt x)dx. Answer = + C 2. Evaluate the indefinite integral (12sin x+4tan x)dx. Answer = + C 3. Evaluate the indefinite integral. (x^7)e^(x^8)dx. Answer = + C Thank you for helping.
  90. Calculus

    online class and I don't know what to do so I posts. Any help is great.Thank you Convert the integral [0,1]∫ [0,√(1-x^2 -y^2)]∫𝑧√(x^2 +y^2 +z^2)dz dy dx into anequivalent integral in spherical coordinates and evaluate the integral.
  91. Calculus

    evaluate the integral or state that it diverges. Check if I did it correctly. integral 0,1 dr/r^.999 lim b->0+ integral b, 1 1000r^.001 =-1000
  92. calculus

    evaluate integral or state that it is diverges integral -oo, -2 [2/(x^2-1)] dx ----------------------------------- integral -oo, -2 [2/(x^2-1)] dx Through partial fractions, I came up with lim [ln(x-1)-ln(x+1)] b, -2 b->-oo I get (ln(3)-0)-(oo-oo)). The
  93. PHYSICS

    Interactive Solution 12.29 presents a model for solving problems of this type. A thin spherical shell of silver has an inner radius of 5.64 x 10-2 m when the temperature is 24.1 °C. The shell is heated to 133 °C. Find the change in the interior volume of
  94. math

    Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form integral cos(9x) dx, u=9x
  95. Calculus 2

    The question is: Evaluate the improper integral for a>0. The integral is: the integral from 0 to infinity, of e^(-y/a)dy Can anyone help me solve this? When I try I get 'a', which apparently is incorrect. Thank you!
  96. Calculus

    Find the volume that is generated by rotating the area bounded by y=x^2 and y=2-x^2 about the x-axis using the shell method.
  97. Calculus

    Verify that the volume of a cylinder of radius r and height h is given be the formula v= pi*r^2*h using cylindrical shell method.
  98. Math

    (i) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using trigonometric substitution. (ii) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using regular substitution. (iii) Use a right triangle to check that indeed both answers you obtained in parts (i) and (ii) are the
  99. math

    Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form integral 2(2x+6)^5 dx, u=2x+6
  100. math

    Evaluate the given integral, where C is the circle with positive orientation. Cauchy integral theorem, integral over C (2z-3)/(z^(2)-4)(z+2) dz, C:|z+3|=3

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