# solid is formed by rotating the region bounded by the curve y=e−3x^2 and the x-axis between x=0 and x=1, around the x-axis. The volume of this solid is 3(1−e^−3). Assuming the solid has constant density , find x and y

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1. ### 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-...
2. ### Calculus

solid is formed by rotating the region bounded by the curve y=e−3x^2 and the x-axis between x=0 and x=1, around the x-axis. The volume of this solid is 3(1−e^−3). Assuming the solid has constant density , find x and y. I know that y bar must be 0. and I got ....
3. ### Calculus

solid is formed by rotating the region bounded by the curve y=e−3x^2 and the x-axis between x=0 and x=1, around the x-axis. The volume of this solid is 3(1−e^−3). Assuming the solid has constant density , find x and y. I know that y bar must be 0. and I got ....
4. ### Calculus

A solid is formed by rotating the region bounded by the curve y=e−3x2 and the x-axis between x=0 and x=1, around the x-axis. The volume of this solid is 3(1−e−3). Assuming the solid has constant density , find x and y. I know that y bar must be 0. and I got ....
5. ### Calculus

Let R be the region bounded by the x-axis, x = 5 and the curve y = x. This region is rotated around the x-axis. Find the volume of the resulting solid. (Note: R is a triangular region. The resulting solid has a simple shape. You may ask me if you are highly unsure about what ...
6. ### Calculus

a) Find the volume formed by rotating the region enclosed by x = 6y and y^3 = x with y greater than, equal to 0 about the y-axis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y = 0 about the x-axis. c) Find the volume of the ...
7. ### 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 ...
8. ### 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 ...
9. ### 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...
10. ### 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...
11. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by y=x^3, y=1, and the y-axis and whose cross-sections perpendicular to the y axis are equilateral triangles. I asked this same question for the y-axis around the x-axis (Thanks for the explanation) but I don...
12. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by y=x^3, y=1, and the y-axis and whose cross-sections perpendicular to the y axis are equilateral triangles. I asked this same question for the y-axis around the x-axis (Thanks for the explanation) but I don...
13. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by y=x^3, y=1, and the y-axis and whose cross-sections perpendicular to the y axis are equilateral triangles. I asked this same question for the y-axis around the x-axis (Thanks for the explanation) but I don...
14. ### 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...
15. ### 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 ...
16. ### Calculus I don't understand

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 10 x and y = 5 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded by y=8 x^2, x = 1, and y = 0 , about the x-axis. I saw some...
17. ### Math calculus 2

Let S be the region of the xy-plane bounded above by the curve ((x^3)*y)=64, below by the line y=1, on the left by the line x=2, and on the right by the line x=4. Find the volume of the solid obtained by rotating S around (a) the x axis (b) the y axis (c) the line x=2
18. ### Calculus I

Find the volume of the solid formed by rotating the region bounded by the graph of y equals 1 plus the square root of x, the y-axis, and the line y = 3 about the x-axis.
19. ### 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 ...
20. ### 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 ...
21. ### 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 ...
22. ### calculus

the base of a solid is a region in the first quadrant bounded by the x-axis, the y-axis, and the line y=1-x. if cross sections of the solid perpendicular to the x-axis are semicircles, what is the volume of the solid?
23. ### calculus

The base of a solid is the region in the first quadrant bounded by the graph of y = 3/(e^x) , the x-axis, the y-axis, and the line x=2. Each cross section of this solid perpendicular to the x-axis is a square. What is the volume of the solid?
24. ### Calculus

R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the cross-sections of the solid perpendicular to the y-axis are squares. Find the volume of the ...
25. ### Calculus

R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the cross-sections of the solid perpendicular to the y-axis are squares. Find the volume of the ...
26. ### Calculus

R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the cross-sections of the solid perpendicular to the y-axis are squares. Find the volume of the ...
27. ### Calculus [Finding volume of solid]

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2 y=0 x=3 about the y-axis
28. ### 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: [...
29. ### 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?
30. ### calculus

Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 9 - 9x^2 , y = 0 Find the volume V of this solid. Sketch the region, the solid, and a typical disk or washer. Any help or tips would be greatly appreciated; not sure how to ...
31. ### Calculus

Use the disk method to find the volume of the solid formed by rotating the region bounded by y=2x and y=x^2 about the y-axis.
32. ### calculus

Use the disk method to find the volume of the solid formed by rotating the region bounded by y=2x and y=x^2 about the y-axis.
33. ### Calculus

Use the disk method to find the volume of the solid formed by rotating the region bounded by y=2x and y=x^2 about the y-axis
34. ### 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.
35. ### calculus

3). The shaded region is bounded by the y-axis and the graphs of y=1+√x, y=2. Find the volume of the solid obtained by rotating this region around the x-axis. Answer choices: 7/6pi, 4/3pi, 11/6pi, 5/3pi, 13/6pi, 5/6pi 4). Find the area of the region bounded by y=x^2-6x+7...
36. ### CALCULUS

Let R be the region bounded by y=e^x, y=2. and the y-axis. Find the volume of the solid obtained by rotating the y-axis.
37. ### Calculus

A base of a solid is the region bounded by y=e^-x, the x axis, the y axis, and the line x=2. Each cross section perpendicular to the x-axis is a square Find the volume of the solid
38. ### calculus

Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 6 x^6 , y = 6 x , x >= 0 Find the volume V of this solid.
39. ### calculus

Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y=6x^5, y=6x, x>or equal to 0 Find the volume V of this solid.
40. ### Calculus II

Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. y = ln x, y = 4, y = 5, x = 0 Find the volume V of this solid. Help!!! Thank you in advance :(
41. ### 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?
42. ### Calculus [rotation of region bounded by curves]

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=3x^2, x=1, y=0 about the x-axis
43. ### calculus

Find the volume of the solid whose base is the region bounded between the curve y=sec x and the x-axis from x=pi/4 to x=pi/3 and whose cross sections taken perpendicular to the x-axis are squares.
44. ### 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
45. ### Math calculus 2

Find the volume of the solid obtained by revolving the region bounded by y=22*x−22*(x^2) and the x-axis around the x-axis.
46. ### Calc 1

The region in the first quadrant bounded by the x-axis, the line x = ln(π), and the curve y = sin(e^x) is rotated about the x-axis. What is the volume of the generated solid?
47. ### 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.
48. ### 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.
49. ### calculus

The base of a solid is bounded by the curve y= sort (x+2) ,the x-axis and the line x = 1. The cross sections, taken perpendicular to the x-axis, are squares. Find the volume of the solid.
50. ### Cal 2

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=1/x^3,y=0,x=4,x=7. About the y-axis. Volume =
51. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by y=x^3, y=1, and the y-axis around the x-axis. What I did was: V=ç(0,1)pi(1-x^3)^2 dx v=pi(x^7/7-x^4/2+x) and I evaluated it for one since 0 is just going to be 0. and I got 9pi/14 The answer is wrong, ...
52. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by y=x^3, y=1, and the y-axis around the x-axis. What I did was: V=ç(0,1)pi(1-x^3)^2 dx v=pi(x^7/7-x^4/2+x) and I evaluated it for one since 0 is just going to be 0. and I got 9pi/14 The answer is wrong, ...
53. ### 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 ...
54. ### Math(cal2)

Find the volume of the solid whose base is the region bounded by the x axis, the curve y=(x^2+9)^(1/2), x=1,x=3 and which has the property that each cross section perpendicular to the x axis is equilateral triangle.
55. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2, x=y^2 about the axis x=–1
56. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2 x=y^2 about the axis x=–5
57. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=0, y=x(3-x) about the axis x = 0
58. ### calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=4 x^2, x = 1, y = 0, about the x-axis
59. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x=4y^2, y=1, x=0 about the y-axis
60. ### math

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x=2y^2 , y=1 ,x=0 about the y-axis
61. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x=2y^2 y=1 x=0 about the y-axis
62. ### CALCULUS:)

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x=3y^2, y=1, x=0 about the y-axis.
63. ### CALCULUS:)

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2, x=y^2 about the axis x=–3
64. ### calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2, y = 0, x = 0, x = 3, about the y-axis
65. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2, y = 0, x = 0, x = 3, about the y-axis
66. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2,x=y^2 about the axis x=–7
67. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=6x^2, x=1, y=0, about the x-axis
68. ### calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed axis. x+y = 3, x = 4−(y−1)^2; about the y-axis.
69. ### Calculus

Find the volume of the solid formed by rotating the region bounded by the graph of y equals 1 plus the square root of x, the y-axis, and the line y = 3 about the line y = 5.
70. ### calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x2x=y2 about the axis x=–3

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=2+1/x^4,y=2,x=4,x=9; about the x-axis.
72. ### calculus

Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed axis. y = 64x−8x^2, y = 0; about the y-axis.
73. ### 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?
74. ### Calculus

Find the volume of the solid formed by rotating the region enclosed by y=e^(1x)+4 y=0 x=0 x=0.3 about the x-axis. I attempted this problem numerous time and kept on getting 5.501779941pi, using the formale integral of pi(r^2) bounded by 0.3 and 0.
75. ### Calculus

The region in the first quadrant bounded by the x-axis, the line x = ln(π), and the curve y = sin(ex) is rotated about the x-axis. What is the volume of the generated solid? Got 2.8 and .79 very confused
76. ### 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
77. ### Math

Find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis? y=x^2 x=y^2 about the axis x=–2 here's what i did and it was incorrect V = 2pi [x+2][x^1/2 - x^2]dx from 0 to 1 V = 2 pi [2x^5/3 / 5 + 4x^3/2 / 3 - x^4/4 - 2x^3 / 3] V...

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 the volume when the ...
79. ### 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.
80. ### Calculus 2b

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2 x=y^2 about the axis x=–3 ? Having Trouble please help!!
81. ### calculus

Find the volume of the solid obtained by rotating the region bounded by y= x^2 and x=y^2 about the x-axis.
82. ### calculus

Find the volume of the solid obtained by rotating the region bounded by y=4x^2,x=1,y=0 about the x-axis.
83. ### cal

Find the volume of the solid obtained by rotating the region bounded by y=4x^2,x=1,y=0 about the x-axis.
84. ### cal

Find the volume of the solid obtained by rotating the region bounded by y=5x+25 y=0 about the y-axis.
85. ### calculus

Find the volume of the solid obtained by rotating the region bounded by y=5x+25, y=0 about the y-axis.
86. ### calculus

Find the volume of the solid obtained by rotating the region bounded by y=5x+25 y=0 about the y-axis.
87. ### calculus

Find the volume of the solid obtained by rotating the region bounded by y=5x+25 and y=0 about the y-axis.
88. ### calculus

Find the volume of the solid obtained by rotating the region bounded by y=5x+25 y=0 about the y-axis.
89. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by y=8x+24, y=0 about the y-axis.
90. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by y= x^2, y=0, and x=3 about the x-axis.
91. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by y= x^2, y=0, and x=3 about the x-axis.
92. ### calculus 2

Find the volume of the solid formed by rotating the region enclosed by y=e^(5x) , \ y=0, \ x=0, \ x=0.8 around the y-axis Please help, i have been attempting these problems for a couple of days
93. ### Calculus AB

Consider the region trapped between the graphs of y=9-x^2 and y=11-3x. a) find the area of this region b) set up an integral which computes the volume of the solid of rotation obtained by rotating this region about the x-axis c) set up an integral which computes the volume of ...
94. ### Calculus AB

Consider the region trapped between the graphs of y=9-x^2 and y=11-3x. a) find the area of this region b) set up an integral which computes the volume of the solid of rotation obtained by rotating this region about the x-axis c) set up an integral which computes the volume of ...
95. ### calculus

Sketch the region bounded by the curves y = x^2, y = x^4. 1) Find the area of the region enclosed by the two curves; 2) Find the volume of the solid obtained by rotating the above region about the x-axis; 3) Find the volume of the solid obtained by rotating the above region ...
96. ### geometry

Sketch the region enclosed by the lines x=0 x=6 y=2 and y=6. Identify the vertices of the region. Revolve the region around the y-axis. Identify the solid formed by the revolution calculate the volume of the solid. Leave the answer in terms of pi.

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 you sure it is to be ...
98. ### calc

The base of a solid in the region bounded by the graphs of y = e^-x y = 0, and x = 0, and x = 1. Cross sections of the solid perpendicular to the x-axis are semicircles. What is the volume, in cubic units, of the solid?
99. ### calculus

help!! please ...Find the volume of the solid obtained by rotating the region bounded by y=5x+25 y=0about the y-axis
100. ### calc

The region in the first quadrant bounded by the x-axis, the line x = π, and the curve y = sin(sin(x)) is rotated about the x-axis. What is the volume of the generated solid?