Posted by **Jamie** on Thursday, July 19, 2012 at 7:19pm.

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

- calculus -
**bobpursley**, Thursday, July 19, 2012 at 7:46pm
as I see it, the upper and lower boundries cross at 5,25, os the integral will be from x=0 t0 5

so the dArea will be [(50-x^2)-x^2]dx

and you will rotate that about the y axis, so the volume will be INT 2PI*xdA or

int 2PI x(50-2x^2)dx

so integrate that. I will be happy to check it.

- Volume -
**MathMate**, Thursday, July 19, 2012 at 7:50pm
Like all multiple integral problems, start with drawing a sketch of the bounding curves.

I have done that for you for this time, see:

http://img687.imageshack.us/img687/811/1342739949.png

If curves intersect, find the intersection points. In this case, it is at (5,25).

Then decide how you want to integrate, namely the order of integrating along x first, followed by y, or vice versa.

Using the ring method, and set up the double integral:

Volume

=∫∫2πx dy dx

y goes from x^2 to 50-x^2 and

x goes from 0 to 5 (intersection point).

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