1. Calc 2

    Find the area of the surface generated when y=4x and x=1 is revolved about the y-axis.
  2. Calc 2 Urgent Surface Area of Revolution Question

    Find the area of the surface generated when y=4x and x=1 is revolved about the y-axis. We have to use the surface area formula of revolution. Integral (2pi*f(x)sqrt(1+f'(x)^2))dx
  3. Calc 2 Urgent Surface Area

    Find the area of the surface generated when y=4x and x=1 is revolved about the y-axis. We have to use the surface area formula.
  4. Calculus check and help

    Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. Find the the area of R. B. Find the value of z so that x=z cuts the solid R into two parts with
  5. CALCULUS problem

    There are four parts to this one question, and would really appreciate if you could show and explain how you get to the answer, because I tried looking up how to find the answer myself, but nothing made sense. Thank you! 11. The region R is bounded by the
  6. Calculus

    The region R is bounded by the x-axis, x = 1, x = 3, and y = 1/x3. a.) Find the area of R. b.) Find the value of h, such that the vertical line x = h divides the region R into two Regions of equal area. c.) Find the volume of the solid generated when R is
  7. Calculus

    The region R is bounded by the x-axis, x = 1, x = 3, and y = 1/x^3. a.) Find the area of R. b.) Find the value of h, such that the vertical line x = h divides the region R into two Regions of equal area. c.) Find the volume of the solid generated when R is
  8. calc

    1. Let R be the region bounded by the x-axis, the graph of y=sqr(x) , and the line x=4 . a. Find the area of the region R. b. Find the value of h such that the vertical line x = h divides the region R into two regions of equal area. c. Find the volume of
  9. Calculus

    Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. Find the the area of R. B. Find the value of z so that x=z cuts the solid R into two parts with
  10. Calculus

    Suppose that the region between the x-axis and the curve y=e^-x for x>=0 has been revolved around the x-axis. Find the surface area of the solid. I got 3*pi The book shows an answer of pi * [sqrt(2) + ln(1 + sqrt(2))] Where do I go wrong? For the sides of
  11. calculus 2

    The curve y=sinh(x),0
  12. Calculus (Solid of Revolution)

    The region R is bounded by the x-axis, x = 1, x = 3, and y = 1/x^3. C. Find the volume of the solid generated when R is revolved about the x-axis.
  13. AP Calculus

    Let R be the region bounded by the x-axis and the graph of y=6x-x^2 Find the volume of the solid generated when R is revolved around the y-axis
  14. calculus

    find the volume generated by the boundaries y=x^3+1 , x-axis , x=1 , x=2 revolved about y-axis
  15. calculus

    Find the surface area of the solid generated by rotating the area between the y-axis, (x^2/y) + y = 1, and -1≤y≤0 is rotated around the y-axis.
  16. calculus1

    Region R is bounded by x=2-2y^2 and x=1-y^2 find the volume of the solid generated if R is revolved about the y-axis Anybody help me with this? thanks!
  17. Calculus

    Let 𝑆 be the region (in the first quadrant) bounded by a circle 𝑥^2 + 𝑦^2 = 2, 𝑦^2 = 𝑥 and the 𝑥-axis (ii) Find the volume of the solid generated by rotating the region 𝑆 about the 𝑦-axis (c) Find the surface area of the solid
  18. calculus

    Find the surface area generated when y = (x^3/12) + (1/x), from x=1 to x=2 is rotated around the x-axis.
  19. Calculus

    Use the disk method to find the volume of the solid generated when the region bounded by y=15sinx and y=0, for 0
  20. calculus

    Sketch the region R bounded by the graphs of the equations and find the volume of the solid generated if R is revolved around the x axis. x= y^2 x-y =2
  21. calculus

    sketch the region R bounded by the graphs of the equations, and find the volume of the solid generated if R is revolved about the x axis when y=x^2 y=4-x^2
  22. calculus

    if the region enclosed by the y-axis, the line y=2 and the curve y=the square root of x is revolved about the y-axis, the volume of the solid generated is????
  23. Math

    Find the area of the surface generated by revolving the curve y = (x + 3)^1/2, 2 ≤ x ≤ 4 about the x-axis.
  24. Math

    Find the volume of the solid generated by revolving the region bounded by y=x+(x/4), the x-axis, and the lines x=1 and x=3 about the y-axis. I've drawn the graph and I understand which part is being rotated, but I'm having trouble setting up the equation.
  25. Calculus

    Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. Find the volume of the solid generated when R is revolved around the line y=pi. B. Fine the volume
  26. Integral Calculus

    Find the area of the surface generated by revolving the given curve about the y-axis. 8xy^2=2y^6+1 , 1
  27. MATH

    Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the following about the given axes. x = y - y3, x = 1, y = 1 (b) Revolved about the y-axis ? Hi Shawn, 97/105 * pi ? :) We need to cut away the volume of the
  28. Calculus

    The graph of the curve y2=10 x+10 is a parabola, symmetric with respect to the x-axis. Find the area of the surface generated by rotating about the x-axis the part of this curve corresponding to 0 ≤ x ≤ 20.
  29. Math

    I am in Calculus and am currently learning how to find the Area of a Surface of Revolution. I cannot understand what the surface of revolution (whether it's the x-axis, y-axis, or y=6) is. For example, I had a problem saying to use the washer method to
  30. Integral calculus

    find the area of the surface generated by revolving about x-axis the upper half of the ellipse 4x^2 + 16y^2 = 64
  31. calculus

    Find the volume when the area bounded by f(x) = xe^x, y = e, and the y-axis, is revolved around the y-axis.
  32. calculs

    Find the volume when the plane area bounded by y=-x^2-3x+6 and x+y-3=0 is revolved about (1) x=3 and (2) about y=o B. Find the volu6 of focus generated by revolving the circule x^2+y^2=4 about the line x=3
  33. University Calculus

    Set up (do not evaluate) the integral that gives the surface area of the surface generated by rotating the curve y=tanhx on the interval (0, 1) around the x-axis. Anyone who can help? Not really sure how to even begin! Thanks
  34. calculus

    Given the area is in the first quadrant bounded by y²=x, the line x=4 and the 0X What is the volume generated when this area is revolved about the 0X? the answer is 25.13 but I don't know how. help me please
  35. Calculus

    This is the questions I have trouble with : Set up (do not evaluate) the integral that gives the surface area of the surface generated by rotating the curve y=tanhx on the interval (0, 1) around the x-axis. Anyone who can help? Not really sure how to even
  36. calculus

    find the volume generated of the region bounded by the parabola y=x^2 and the line y=b when revolved (b>0): a.) about the x-axis b.) about the line y=-1 c.) about the line y=a, where a>b
  37. calculus

    2. Let R be the region of the first quadrant bounded by the x-axis and the cuve y=2X-X^2 a. Find the volume produced when R is revolved around the x-axis b. Find the volume produced when R is revolved around the y-axis
  38. asdf

    Find a definite integral indicating the area of the surface generated by revolving the curve y = 3√3x ; 0 ≤ y ≤ 4 about the x – axis. But do not evaluate the integral.
  39. CALCULUS

    The region R is bounded by the x-axis, y-axis, x = 3 and y = 1/(sqrt(x+1)) A. Find the area of region R. B. Find the volume of the solid formed when the region R is revolved about the x-axis. C. The solid formed in part B is divided into two solids of
  40. CALCULUS HELP PLZ

    The region R is bounded by the x-axis, y-axis, x = 3 and y = 1/(sqrt(x+1)) A. Find the area of region R. B. Find the volume of the solid formed when the region R is revolved about the x-axis. C. The solid formed in part B is divided into two solids of
  41. Calc

    Set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the x-axis. y = (x³/6) + (1/2x), 1≤ x ≤ 2
  42. Calculus

    The region enclosed by the graph of y = x^2 , the line x = 2, and the x-axis is revolved abut the y-axis. The volume of the solid generated is: A. 8pi B. 32pi/5 C. 16pi/3 D. 4pi 5. 8pi/3 I solved for x as √y and set up this integral: 2pi * integral from
  43. Calculus

    The region enclosed by the graph e^(x/2), y=1, and x=ln(3) is revolved around the x-axis. Find the volume of the solid generated. I don't understand if we have to use the washer method or the disk method for this one because when I drew it out on a graph
  44. Calculus

    The region enclosed by the graph e^(x/2), y=1, and x=ln(3) is revolved around the x-axis. Find the volume of the solid generated. I don't understand if we have to use the washer method or the disk method for this one because when I drew it out on a graph
  45. Calc

    Set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the y-axis. y = cube rt. (x) + 2 Thank you so much!!
  46. math

    Find the volume generated by rotating the area between y = cos( 3 x ) and the x axis from x = 0 to x = π/ 12 around the x axis
  47. integral calculus

    find the volume of the solid generated by revolving the area by the given curves about the indicated axis of revolution y^2=4ax,x=a;about the y-axis.
  48. integral calculus

    find the volume of the solid generated by revolving the area by the given curves about the indicated axis of revolution y^2=4ax,x=a;about the y-axis
  49. Math (Calculus II) (Volume Revolution Setup)

    Consider the graph of y^2 = x(4-x)^2 (see link). Find the volumes of the solids that are generated when the loop of this graph is revolved about (a) the x-axis, (b) the y-axis, and (c) the line x = 4. goo.gl/photos/v5qJLDztqsZpHR9d7 I'm just having trouble
  50. calculus

    The region A is bounded by the curve y=x^2-5x+6 and the line y = -x + 3. (a) Sketch the line and the curve on the same set of axes. (b) Find the area of A. (c) The part of A above the x-axis is rotated through 360degree about the x-axis. Find the volume of
  51. 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
  52. 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
  53. Calculus

    The area bounded by the curve y^2 = 12x and the line x=3 is revolved about the line x=3. What is the volume generated?
  54. Calculus HELP plz

    Find the area of the surface obtained by rotating the curve y=sqrt(4x) from x=0 to x=1 about the -axis. about the x-axis. surface area= ⌠ 2pi * f(x)*sqrt[1 + (f'(x))^2] dx from a to b ⌡ it's been 45 years since I used that formula. I ended up with the
  55. calculus

    let R be the region of the first quadrant bounded by the x-axis and the curve y=2x-x^2. Find the volume produced when R is revolved around the X-axis
  56. math

    The region in the first quadrant bounded by the 𝑦-axis and the curve 𝑥 = 2𝑦2 − 𝑦3 (graph please) is revolved about the 𝑥-axis. Find the volume?
  57. calculus

    Let R be the region in the first quadrant bounded by the graphs of y=e^-x, y=1/2x+1, and x=2. Then find the volume of the solid when R is revolved about each of the following lines... the x axis, y=-1, y=2, the y axis, x=-1, and x=3.
  58. Calculus

    This is a question from my textbook that does't have a solution and quite frankly I have no idea what to do. Any tips would be greatly appreciated. Given the function f defined by f(x) = 9 - x^2. Find the surface area bounded by the curve y = f(x), the x
  59. Solids of Revolution

    The region enclosed by the curve y =e^x, the x-axis, and the lines x=0 and x=1 is revolved about the x-axis. Find the volume of the resulting solid formed.
  60. Math

    The region enclosed by the curve y = ex, the x-axis, and the lines x = 0 and x = 1 is revolved about the x-axis. Find the volume of the resulting solid formed. How do you do this?
  61. Calculus

    Let R be the region bounded by y=x^2, x=1, and y=0. Use the shell method to find the volume of the solid generated when R is revolved about the line y=-2.
  62. Calculus

    Let R be the region bounded by y=x^2, x=1, and y=0. Use the shell method to find the volume of the solid generated when R is revolved about the line x=-11.
  63. Calculus

    The following are about an infinite region in the 1st quadrant between y=e^-x and the x-axis. A) Find the area of the region B)Find the volume of the solid generated by revolving the region about the y-axis
  64. Math

    Find the volume generated if the region bounded by y = sin 2x and y = cos x, π/6 ≤ x ≤ π/2 is revolved about the line y = 2. Use the method of washers.
  65. Math

    Find the volume of the solid generated by rotating the area bounded by y=x^2 and x=y^2 about the x-axis.
  66. Math

    Find the volume of the solid generated by rotating the area bounded by y=x^2 and x=y^2 about the x-axis.
  67. Calculus

    Let R be the region bounded by the y-axis and the curves y = sin x and y = cos x. Answer the following. a)Find the exact area of R. b)A solid is generated by revolving R about the x-axis. Find the exact volume of the solid.
  68. Calculus

    Let R be the region bounded by the y-axis and the curves y = sin x and y = cos x. Answer the following. a)Find the exact area of R. b)A solid is generated by revolving R about the x-axis. Find the exact volume of the solid.
  69. 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.
  70. Math - Calculus

    Find the area of the surface of revolution generated by revolving the curve y = 3 sqrt (x), 0
  71. Math

    Find the volume generated when the area bounded by the curve y^2 = 16x, from x = 0 to x = 4 is rotated around the x-axis.
  72. Calculus Help!!

    Region R is bounded by the functions f(x) = 2(x-4) + pi, g(x) = cos^-1(x/2 - 3), and the x axis. a. What is the area of the region R? b. Find the volume of the solid generated when region R is rotated about the x axis. c. Find all values c for f(x) and
  73. calculus

    Find the volume of the solid generated by revolving the region about the given line. The region in the second quadrant bounded above by the curve y = 16 - x2, below by the x-axis, and on the right by the y-axis, about the line x = 1 I have gathered, that
  74. Calculus

    Find the volume of the solid generated by rotating about the y axis the area in the first quadrant bounded by the following curve and lines. y=x^2, x=0, y=2.
  75. Calculus

    Find the volume generated by rotating about the x axis the area bounded by x=0, y=2sinxcosx,, y=2cosx, and x=4, if 0≤x≤pi/2. I don't get the graph.
  76. Integral calculus

    Use the cylindrical shell method to find the volume of the solid generated by revolving the area bounded by the given curves (x-3)^2 + y^2 = 9, about y-axis.
  77. math

    Let S be a region bounded by the curve y=x+cosx and the line y=x as shown in the given figure. Find the volume of the solid generated when S is rotated about the x-axis. Find the volume of the solid generated when S is rotated about the y-axis.
  78. calculus

    Consider the graph of y2 = x(4 − x)2 (see figure). Find the volumes of the solids that are generated when the loop of this graph is revolved about each of the following
  79. calculus

    Consider the graphs of y = 3x + c and y^2 = 6x, where c is a real constant. a. Determine all values of c for which the graphs intersect in two distinct points. b. suppose c = -3/2. Find the area of the region enclosed by the two curves. c. suppose c = 0.
  80. Integral Calculus

    Volume of the area bounded by y=sin(x), x-axis, x is greater than or equal to 0 but less than or equal to pi, revolved about x=3pi/2.
  81. Calculus

    This is another textbook number that doesn't have the solution and I can't figure it out. Any tips would be greatly appreciated. For each of the plane surfaces, calculate the exact surface area. (Answer in fractions) (a)The surface composed of all surfaces
  82. calculus

    Let A be the region bounded by the curves y=x^2-6x+8 and y=0, find the volume when A is revolved around the x-axis
  83. calculus

    Find the volume of the solid bounded by the curves y = 4 - x^2 and y = x revolved about the x axis.
  84. Maths

    A.Find the area of the region bounded above by y=2cosx and above by y=secx,-π/4≤x≤π/4. B.Find the volume of the sold generated by revolving the region in (A) above about the x-axis
  85. Math

    A rectangular strip 25cm*7cm is rotated about the longer side. find the total surface area of the solid thus generated.
  86. Calculus

    I would like to know if my answers are correct: Disclaimer: We are allowed to keep our answers in formula form 1. Use the washer method to find the volume of the solid that is generated by rotating the plane region bounded by y=x^2 and y = 2-x^2 about the
  87. Calc 2

    The region bounded by y= 1/(x^2+2x+5), y=0, x=0, and x=1, is revolved about the x-axis. Find the volume of the resulting solid.
  88. Calculus

    Let A be the region bounded by the curves y = x^2-6x + 8 and y = 0. Find the volume obtained when A is revolved around the Y-AXIS
  89. Calculus

    Find the volume of the solid formed when the region bounded by y=3x^2 and y=36-x^2 is revolved about the x-axis.
  90. calculus

    Find the volume of the solid that is obtained when the region under the curve y = 4 − x^2/6 is revolved around the y -axis between y = 0 and y = 4 .
  91. calculus 2

    The region bounded by y=e^(-x^2),y=0 ,x=0 ,x=1 and is revolved about the y-axis. Find the volume of the resulting solid.
  92. Calculus

    Let A be the region bounded by the curves y = x^2-6x + 8 and y = 0. Find the volume obtained when A is revolved around the Y-AXIS
  93. calculas

    Find the volume of the solid that is obtained when the region under the curve y=©ø¡îx+3 over the interval [5, 24] is revolved about x-axis.
  94. Geometry/Algebra/Calculus

    Why isn't the surface area of a sphere with radius r the following: 2*pi * (pi*r) That comes from the following flow of logic: Doesn't it makes sense to think of the surface area of the sphere with radius r as the the circumference of the semi-circle with
  95. maths

    the region in the first quadrant bound by the graphs y=(x*x*x)/3 and y=2x is revolved about the y-axis. find the volume of the resulting solid.
  96. Calculus Shell method 2

    Use cylindrical shells to find the vol of the solid that results when the region enclosed by y=x^3-5x^2+6x over [0,2] is revolved about the y axis
  97. Calculus Shell method

    Use cylindrical shells to find the vol of the solid that results when the region enclosed by y=x^2, y=4 and x=0 is revolved about the x axis
  98. Calculus

    5. Find the volume of the solid generated by revolving the region bounded by y = x2, y = 0 and x = 1 about (a) the x-axis (b) the y-axis
  99. Calculus II

    Find the volume of the solid generated by revolving the triangular region with vertices (1,1), (b,1), and (1,h) about: a) the x-axis b) the y-axis
  100. Calculus

    Find the volume of the solid generated by the region in the first quadrant bounded above by the 3x+y=6, below by the x-axis, and on the left by the y-axis, about the line x= -2.