# Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y=ln x, y=0, x=1, x=3 Please show the steps in your work, thanks! :)

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1. ### Calculus

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y=ln x, y=0, x=1, x=3 Please show the steps in your work, thanks! :)
2. ### Calculus

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y=ln x, y=0, x=1, x=3 Please show the steps in your work, thanks! :)
3. ### calculus

find the volume of the solid generated by revolving the region bounded by the graphs of the equations y=2sqrtx, y=o, x=3 about the x-axis.
4. ### calculus

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations and/or inequalities about the indicated axis. x = y(25 − y2)^1/2 x = 0 the y-axis
5. ### Calculus Voulme

find the volume of the solid generated by revolving the region r bounded by the graphs of the given equations about the y-axis. x^2+y^2=1 x=1 y=1
6. ### Math (Calculus)

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis. (Use Disc Method) y=3(2-x), y=0, x=0
7. ### calculus

1. Find the area of the region bounded by f(x)=x^2 +6x+9 and g(x)=5(x+3). Show the integral used, the limits of integration and how to evaluate the integral. 2. Find the area of the region bounded by x=y^2+6, x=0 , y=-6, and y=7. Show all work required in #1. 3. Find the ...
8. ### calculus

Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. y = x3 y = 0 x = 3 the x-axis,the y-axis,and the line x = 4
9. ### Calculus 2

Find the volume of the solid generated by revolving the region bounded by the graphs of the quations about the x-axis. Y=x^2+4 Y=-x^2+2x+8 X=0 X=3
10. ### Math (Calculus)

Use the disc method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. y=x^3, y=0, x=2 a)the x-axis b)the line x=4
11. ### calculus

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 6. y = 6 − x y = 0 y = 5 x = 0
12. ### Calculus

Find the volume or the solid generated by revolving around the region bounded by the graphs of the equations about line x=6. xy=6, y=2, y=6, and x=6
13. ### Calc

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = sin x, y = 0, x = 0 I just need help setting up the formula. So far I got V= the integral from 0 to pi of [(sin²x) - 0²]dx. Is that correct? Thank you ...
14. ### Calculus

"Find the volume of the solid generated by revolving the region bounded by the graphs of the given equations about the indicated lines: y = 2x^2 y = 0 x = 2 About the line y = 8"
15. ### calculus

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. (Round your answer to three decimal places.) y = e^−x y=0 x=0 x=7 I got the answer ~10.783 Idk why it's wrong
16. ### Calculus

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = 0.5x^2, y = 2, and x = 0 about the line y = 2. A. 8pi/15 B. 32pi/15 C. 64pi/15 D. 4pi/15 E. 16pi/15
17. ### 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 axis y=-1 My Work: [...
18. ### 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
19. ### college, math

find the bolume of the solid generated by revolving the region bounded by the graphs of y=sqrt x , y=0, and x=4 about the x axis
20. ### Calculus

Can you please check to see if these answers are correct? I have provided my work as well! That you! This is much appreciated!! 1. What is the volume of the solid that is generated by revolving the region bounded by the curves x = 3y^2-2 and x = y^2 and y = 0 about the x axis...
21. ### calculus

Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. y = x3 y = 0 x = 3 a)the line x = 4
22. ### poly

the volume of the solid generated by revolving infinite region bounded by x-axis, x=k, and y=1/x+2 in the first quadrant about the x-axis to generate a solid. Find the volume of the solid.
23. ### Calc Desperate

can anyone help me with the last problem # 14 Find the volume of the given solid generated by revolving the regions bounded by the graphs of the equations about the given lines. 14. y=6-2x-x^2, y=x+6 a. the x-axis b. the line y=3
24. ### 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
25. ### calc

Find the volume of the solid generated by revolving the region bounded by y=e^(5/2x),y=0,x=1, and x=5 about the x-axis.
26. ### Volume of a solid - calculus

Find the volume of the solid generated by revolving the region bounded by the curves: y=2 Sqrt(x), y=4, x=0 about the x-axis
27. ### Calculus

find the volume of the solid formed by revolving the region bounded by the graphs of y=x^3 y=1 x=2 about the y-axis
28. ### math

Find the volume of the solid generated by revolving the region bounded by y= x^(1/2), y= 0, and x= 3 revolving around the y-axis.
29. ### Calculus

'Find the volume of the solid generated by revolving the region bounded by x=16-y^2, x-axis, and y-axis around the x-axis.' I know in theory how to do it, but I'm a little confused by what constitutes the bounded region because it's a sideways parabola, but if the x-axis is a ...
30. ### 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 region you get by ...
31. ### Volume

Find the volume of the solid generated by revolving the region bounded by the given curves and line about the y-axis. y=50-x^2 y=x^2 x=0

1) A region is bounded by the line y = x and the parabola y = x2 - 6x + 10. What is the volume of the solid generated by revolving the region about the x-axis? would u please give the explanation with a detailed steps to the answer because i am not able to reach the final ...
33. ### Calculus

Find the volume of the solid formed by revolving the region bounded by the graphs of y=4x^2 and y=16 about the x-axis. (Washer Volume)
34. ### 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
35. ### 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 find the volume of the ...
36. ### Math

Find the volume of the solid generated by revolving the region bounded by y= 5 cosh (x) and y= 5 sinh (x) between x = 0 and x = 1 about the x-axis
37. ### math

1) A region is bounded by the line y = x and the parabola y = x2 - 6x + 10. What is the volume of the solid generated by revolving the region about the x-axis?
38. ### math

1) A region is bounded by the line y = x and the parabola y = x2 - 6x + 10. What is the volume of the solid generated by revolving the region about the x-axis?
39. ### cal

Solve the problem. Find the volume of the solid generated by revolving the region bounded by the curve y=lnx, the x-axis, and the vertical line x=e^(2) about the x-axis.
40. ### math

Find the volume of a solid generated by revolving the region bounded by y=secx and y=0 and x=0, x-pi/4 about the x axis. Don't evaluate. Please help!!!! Also, what si the average value of this equation? I don't understand what that means.
41. ### Calculus

Find the volume of the solid generated by revolving the following region about the given axis. The region in the first quadrant bounded by the curve y=x^2, below by the x-axis, and on the right by the line x=1, about the line x=-2
42. ### Math

Find the volume of the solid generated by revolving the following region about the given axis The region in the first quadrant bounded above by the curve y=x^2, below by the x-axis and on the right by the line x=1, about the line x=-4
43. ### calculus

Give the volume of the solid generated by revolving the region bounded by the graph of y=ln(x), the x-axis, the lines x=1 and x=e, about the y-axis
44. ### Calculus

Use the disk method to find the volume of the solid generated by revolving about the y-axis the region bounded by the curves y=8−x^2 and the curve y=x^2.
45. ### 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.
46. ### 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.
47. ### 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 washer method is to be...
48. ### Calculus

This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume of the solid formed by rotating around the x-...
49. ### Calculus

We're learning disks, shells, and cylinders in school but we have a substitute and I've been trying to teach this to myself. Can you check them please? =) Thank you! 1) Find the volume of the solid formed when the region bounded by curves y=x^3 + 1, x= 1, and y=0 is rotated ...
50. ### Calculus

We're learning disks, shells, and cylinders in school but we have a substitute and I've been trying to teach this to myself. Can you check them please? =) Thank you! 1) Find the volume of the solid formed when the region bounded by curves y=x^3 + 1, x= 1, and y=0 is rotated ...
51. ### calculus

Find the volume of the solid generated by revolving the region about the given line. The region is in the first quadrant bounded above by the line y= sqrt 2, below by the curve y=secxtanx, and on the left by the y-axis. Rotate the region about the line y=sqrt 2. i also need to...
52. ### Calculus

Find the volume of the solid formed by revolving the region bounded by the graphs of y = x^2, x = 4, and y = 1 about the y-axis. I'm supposed to use this equation right? piR^2-x^r^2. and then change y=x^2 to x=sqrty. That's all I got.
53. ### Can no one help?!

1. Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by y= 2x and y = x^2 -3 about x= 6. 2. Find the volume of the solid formed by revolving the region bounded by y= e^x , y= e^-x, and y= 3 about y= 5. I'm desperately trying to ...
54. ### Calculus

1. Find the volume formed by rotating the region enclosed by x=5y and x=y^3 with y¡Ý0 about the y-axis. 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis y=18x-6x^2 , y=0 : about the y-axis. PLease can anyone...
55. ### AP Calculus AB

Find the volume of the solid formed by revolving the region bounded by the graphs of y = x^2, x = 4, and y = 1 about the y-axis 39pi/2 225pi/2 735pi/2 None of these I got 39pi/2
56. ### calculus

Find the volume of the solid generated by revolving about line x = -4 the region bounded by x = y - y^2 and x = y^2 - 3
57. ### Calculus

Find the volume of the solid formed by revolving the region bounded by y=x^3, x=2 and y=1 about the y-axis. Please help =(
58. ### Calculus volume stuff

Find the volume of the solid obtained by rotating the region bounded y = 16 x and y = 2 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded about the x-axis by y=4x^2, x =1, and y = 0 Find the volume of the solid generated by rotating the region...
59. ### CALCULUS MAJOR HELP!!!!!!

Find the volume of the solid obtained by rotating the region bounded y = 16 x and y = 2 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded about the x-axis by y=4x^2, x =1, and y = 0 Find the volume of the solid generated by rotating the region...
60. ### 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
61. ### calculus

Find the volume of the solid formed by revolving the region bounded by the graphs of y=3-(x^2) and y=2 about the line y=2
62. ### calculus 2

find the volume of the solid obtained by revolving the region bounded by the graphs of y=2+4x-x^2 and y=2 about the line y=2.
63. ### 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 equal volume by a plane ...
64. ### math

Finf the volume of the solid generated by revolving the region bounded by the curve. x=2/(y+1), x=0, y=0, y=3, about y-axis. My ans is pie unit^3. Is it correct? if wrong can i know the right calculation.
65. ### 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 equal volume by a plane ...
66. ### calculus

1. Let R be the region in the first quadrant enclosed by the graphs of y=4-X , y=3x , and the y-axis. a. Find the area of region R. b. Find the volume of the solid formed by revolving the region R about the x-axis.
67. ### Math

Find the volume of the solid of revolution obtained by revolving the plane region R bounded by y= x^5, the y-axis, and the line y=3 about the x-axis I've gotten 15/7(3^(2/5))pi, but it's not right. Please help
68. ### Calc 2

Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y = x + 2 and the parabola y = x^2 about the following lines: a) The line x=2 b) The line x=-1 c) The x axis d) The line y=26 I know what the formulas are, but I can't ...
69. ### calculus

Find the volume generated by revolving the region bounded by y=18x-3x^2 and y=9x about the y-axis. a. pi/12 b. pi/6 c. 3pi/4 d. pi/3 help! .. :D
70. ### 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.
71. ### Calculus

Find the volume of the solid generated by revolving the region bounded by the line y=5x+6 and the parabola y=x^2 about the following lines: a) the line x=6 b) the line x=-1 c)the x axis d) the line y=36 Thanks!
72. ### Calculus

1. Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by y= 2x and y = x^2 -3 about x= 6. 2. Find the volume of the solid formed by revolving the region bounded by y= e^x , y= e^-x, and y= 3 about y= 5.
73. ### Math

Find the volme of the solid generated by revolving the region bounded by the triangle with vertices (1,1) (1,3) and (2,3) about the x axis using shells and washers.
74. ### 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. Because there is a ...
75. ### 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
76. ### 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.
77. ### Calculus

The region R is in the first quadrant and bounded by the x-axis, the y axis, and y= 3+2x-x^2. Find the volume of the solid that results when R is revolving about y+1= 0
78. ### calculus edit

1. Find the volume formed by rotating the region enclosed by x=5y and x=y^3 with y is greater than or equal to 0 about the y-axis. 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis y=18x-6x^2 , y=0 : about the ...
79. ### calculus

Find the volume generated by revolving about the x-axis the region bounded by the following curves y=sqrt/(4x+3),x=0,x=4, and y=0. (Use "pi" for π).
80. ### calculus

Find the volume of the solid generated by revolving the region delimited by 5x+5y=40, y=0, and x=0 about the x-axis.
81. ### calculus

determine the volume of the solid of revolution generated by revolving the region bounded by y=x^3-x^5, y=0, x=0 and x=1 about the line x=3
82. ### Pre Calc

Find the volume of the solid formed by revolving the region bounded by y = 16 - x^2 and y = 0 about the x-axis .
83. ### Calculus

The following are about an infinite region in the 1st quadrant between y=e^-x and the x-axis. B)Find the volume of the solid generated by revolving the region about the y-axis Part A was solved below. Does anyone know how to do Part B?
84. ### 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 apply
85. ### Calculus I

Which of the following represents the volume of the solid formed by revolving the region bounded by the graphs of y =x^3, y = 1, and x = 2, about the line x = 2?
86. ### Calculus

Find the volume of the solid generated by revolving the region enclosed in the triangle with vertices (4.6,4.6), (4.6,0), (6.7,4.6) about the x-axis.
87. ### Calculus

Let R be the square region bounded by y = 2, x = 2, and the x and y-axes. When R is rotated about the x-axis, what is the volume of the resulting solid? What is the volume of the solid generated by rotating R about the y-axis?
88. ### Calculus - Integrals

Find the volume of the solid of revolution obtained by revolving region bounded by the parabolas 2y=x^2 and y^2=4x about the x-axis
89. ### Calculus (Solid of Revolution)

The region R is bounded by the x-axis, x = 2, and y = x^2. What is the the volume of the solid formed by revolving R about the line x = 2?
90. ### Calculus - HELP URGENT PLEASE

The region R is bounded by the x-axis, x=2 and y=x^2. Which of these expressions represents the volume of the solid formed by revolving R about the line x=2?
91. ### 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!
92. ### Halfway solved-calc

So I'm trying to solve this problem but one thing I don't get is, how do I know which method to use just by looking at the graph (disk, washer, or shell)? Find the volume of the solid generated by revolving the region bounded by the graphs y=x^2- 4x+ 5 and y= 5-x about the ...
93. ### Calculus AP

Let R be the region bounded by the graphs of y=cos((pi x)/2) and y=x^2-(26/5)x+1. A. Find the area of R. B. The vertical line x=k splits the region R into two equal parts. Write, but do not solve, an equation involving integrals that solves for k. C. The region R is the base ...
94. ### CALC

Find the volume of the solid obtained by revolving the region bounded by y=(19/3)x-(19/3)x^2 and the x-axis around the x-axis. Keep answer in terms of pi PLease explain each step
95. ### 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 g(x) in the closed ...
96. ### calculus

Consider the region bounded by the parabola y=x^2 and the line y=16 . (a) What is the volume of the solid generated when revolving this region about the line y=16 ?
97. ### 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.
98. ### 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.
99. ### calculus

find the volume of the solid formed by revolving the region bounded by the graphs of y=x^3,y=1, and x=2 about the x-axis using the disk method. 9 express the answer in terms of pie) i got the answer to be 3/5 pie but im not sure if is right. i used the formula V=(pie)(r)^2W
100. ### calc

Find the volume of the solid generated by revolving the given region in the 1st quadrant about the y-axis: y=10x^2,x=0,y=810.