# Math Help - Volume and disk/washer method

1. ## Volume and disk/washer method

Hey all,

Would anyone be able to halp me with this:

Question:
Using the disk/washer method, find the volume of the solid by rotating y=x^2+1 and y=3-x^2 region about the x-axis.

I got pi*(164/15)

Thanks for the help!! cheers.

2. Originally Posted by klooless
Hey all,

Would anyone be able to halp me with this:

Question:
Using the disk/washer method, find the volume of the solid by rotating y=x^2+1 and y=3-x^2 region about the x-axis.

I got pi*(164/15)

Thanks for the help!! cheers.
find points of intersection ...

$x^2+1 = 3-x^2$

$x = \pm 1$

washer method integral ...

$V = \pi \int_a^b [R(x)]^2 - [r(x)]^2 \, dx$

using symmetry ...

$V = 2\pi \int_0^1 (3-x^2)^2 - (x^2+1)^2 \, dx = \frac{32\pi}{3}$

3. Thank you much for this guide!

Cheers!