Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = 3e^(x), y = 3, x = 2;
about y = 6
 👍
 👎
 👁
 ℹ️
 🚩
1 answer

Using discs (washers) of thickness dx,
v = ∫[0,2] π(R^2r^2) dx
where R=6y and r=3
v = ∫[0,2] π((63e^(x))^23^2) dx
= 9π(5e^4+8e^21)/(2e^4)
using washers of thickness dy,
v = ∫[3/e^2,3] 2πrh dy
where r=6y and h=2x
v = ∫[3/e^2,3] 2π(6y)(2+ln(y/3)) dy
= 9π(5e^4+8e^21)/(2e^4) 👍
 👎
 ℹ️
 🚩
answered by Steve
Answer this Question
Related Questions

calculus
1. Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = sin(x), y = 0, π/2 ≤ x ≤ π; about the x−axis 2. Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = 3
 asked by Anonymous
 4,170 views

Calculus
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. x = 7y^2, y ≥ 0, x = 7; about y = 2
 asked by sp
 14,092 views

calculus
Find the volume of the solid obtained by rotating the region bounded by the curves y = x^8, y = 1 about the line y = 5.
 asked by maggie
 5,943 views

Calculus
Find the volume of the solid obtained by rotating the region bounded by the curves y=cos(x), y=0, x=0, and x=π/2 about the line y=1.
 asked by Ayaka
 3,614 views

Math
what is the volume of the solid obtained by rotating the region bounded by y=x^2, and y=5x about the line x=5 using the washer method and respect to dy?
 asked by Anonymous
 1,483 views

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 yaxis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y = 0 about the xaxis. c)
 asked by Beth
 3,857 views

Calculus
Find the volume of the solid obtained by rotating the region enclosed by y=x^3, y=25x, x ≥ 0
 asked by John
 2,646 views

Calculus
Find the volume of the solid obtained by rotating the region under the graph of f(x)= 9x^2 for 0
 asked by Rucha
 1,205 views

Calculus 2
Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=1/x, y=0, x=1 and x=4 about the line y=−1
 asked by RaShawnya
 2,680 views

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 yaxis. 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis
 asked by jimmy
 1,361 views

Math
Find the volume of the solid obtained by rotating the region enclosed by y=x^2, y=6x about the line x=0using the method of disks or washers.
 asked by Leslly
 3,557 views

Math
The volume of the solid obtained by rotating the region bounded by y=e^x, y=Inx, x=1, and x=2 about the line yaxis can be computed using the method of cylindrical shells. Using the method of cylindrical shells find the volume.
 asked by Lexi
 1,034 views

calculus
Find the volume of the solid formed by rotating the region enclosed by y=e2x+1, y=0, x=0, x=0.9 about the yaxis.
 asked by carlton
 3,115 views

Calculus :)
Find the volume of the solid formed by rotating the region enclosed by y=e^(3x)+2, y=0, x=0, x=0.4 about the xaxis.
 asked by Brit
 3,582 views

Calculus
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the? Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 8. 27y = x^3, y = 0,
 asked by John
 2,676 views

calculus
Consider the solid obtained by rotating the region bounded by the given curves about the xaxis. 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
 asked by Tina
 4,050 views

calc
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=0, y=cos(7x) , x=π/14, x=0 about the axis y=−8
 asked by anonymous
 1,055 views

Math
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 8 sin x, y = 8 cos x, 0 ≤ x ≤ π/4; about y = −1
 asked by Em
 9,727 views

calculus 2
The region bounded by y=e^(x^2),y=0 ,x=0 ,x=1 and is revolved about the yaxis. Find the volume of the resulting solid.
 asked by Nycw
 4,615 views

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 yaxis. y=x, y=3x, y=6 Set up the integral that gives the volume of the solid. Use increasing
 asked by Anonymous
 1,817 views
Still need help?
You can ask a new question or browse existing questions.