Volume by Disks/Washers

Quote:

Originally Posted by jhcasey815

Having an issue with a volume problem, was hoping I could get some help, please. I've got everything figured out on this one, except the limits of integration:

y=2, y=9-X^2 Rotated about y=-1

Normally, I would figure out the points on intersection by setting

9-X^2=2.

Solving this gives me X= +/- Square Root of 7. But when I set my limits to [-sqrt_7,+sqrt_7] they were marked as wrong.

What gives?

Hi jhcasey815,

You could rotate the part of the curve above y=2 around the line y=-1,
or the part of the curve between y=-1 and y=2.

Are you sure which one it is?

If you are rotating the top part above y=2,
you can rotate from x=0 to x= $\sqrt{7}$
and double, or rotate from x= $-\sqrt{7}$ to $\sqrt{7}$

Since the disc radii are $9-x^2-(-1)=10-x^2$
it's also possible to rotate $10-x^2$ above y=3 about the x-axis, if you are rotating the top section.

Do you have the full question?