# Calculus

Find the volume of the solid obtained by rotating the region enclosed by the graphs x=y^(3) and x= y^(1/3) about the y-axis over the interval [0,1].

1. 👍 0
2. 👎 0
3. 👁 106
1. ⌠pi[(y^1/3)^2 - (y^3)^2] dy

= pi INT [y^2/3 - y^6)dy

= pi[(3/5)y^5/3 - (1/7)y^7]│ from 0 to 1

=pi (3/5 - 1/7)
= 16pi/7

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### calculus

Let A be the bounded region enclosed by the graphs of f(x) = x , g(x) = x3 . Find the volume of the solid obtained by rotating the region A about the line x + 2 = 0.

asked by me on October 31, 2010
2. ### Calculus

Find the volume of the solid obtained by rotating the region enclosed by the graphs of y=18-x, y=3x-6 and x=0 about the y-axis V=

asked by Anonymous on December 2, 2016
3. ### Calculus

Find the volume of the solid obtained by rotating the region enclosed by the graphs of y=15-x, y=3x+11 and x=0 about the y-axis.

asked by Al on December 4, 2007
4. ### Calculus

Find the volume of the solid obtained by rotating the region enclosed by the graphs x=y^{5} and x=5sqrty about the y-axis over the interval [0,1].

asked by Claire on March 4, 2017
5. ### 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

asked by Jillian on April 5, 2008
6. ### 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

asked by Megan on June 9, 2011
7. ### 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 =

asked by Beth on November 3, 2011
8. ### 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

asked by jimmy on May 4, 2007
9. ### 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

asked by jimmy on May 4, 2007
10. ### Calculus

Find the volume of the solid obtained by rotating the region enclosed by y=x^3, y=25x, x ≥ 0

asked by John on November 1, 2012

More Similar Questions