# Volume and disk/washer method

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• July 2nd 2009, 04:49 PM
klooless
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.
• July 2nd 2009, 05:01 PM
skeeter
Quote:

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 ...

$V = 2\pi \int_0^1 (3-x^2)^2 - (x^2+1)^2 \, dx = \frac{32\pi}{3}$
• July 2nd 2009, 05:23 PM
klooless
Thank you much for this guide!

Cheers!