# 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.

1. The bounded region is x =0 to x = 1, so those are your limits of integration.

The integral is of
pi*(x^2 - sqrt x)^2 dx.

Visualize it as a stack of washers with holes in the middle.

posted by drwls
2. I think that
the volume=pi*Int(from 0 to 1) (sqrt(x))^2dx-pi*Int(0 to 1)(x^2)^2dx=
pi(1/2-1/5)

posted by Mgraph
3. Mgraph is correct. I should have written
Integral of pi[(sqrtx)^2 - (x^2)^2] dx
0 to 1

which is pi*(1/2 - 1/5)

posted by drwls
4. Thank you so much that makes alot of since.

posted by Anonymous

## Similar Questions

1. ### 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,
2. ### 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 =
3. ### 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
4. ### 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
5. ### 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
6. ### 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
7. ### 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
8. ### 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.
9. ### 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
10. ### CALCULUS 2

Consider the solid obtained by rotating the region bounded by the given curves about the line x = 1. y = x, y = 0, x = 4, x = 6 Find the volume V of this solid
11. ### calculus

Consider the solid obtained by rotating the region bounded by the given curves about the line x = 4. x= 4y^2 , x = 4 Find the volume V of this solid.

More Similar Questions