Homework Help: AP Calculus

Posted by TJ on Sunday, March 22, 2009 at 6:04pm.

I need help with Volume of Revolutions. The question is: Find the volume of the solid generated bt rotating about the designated line the region bounded by:
1. y= x squared + 2, x = negative 1, x = 1 about y = 1.

AP Calculus - Reiny, Sunday, March 22, 2009 at 10:55pm
you will get the same solid if you rotate y = x^2 + 1 about the x-axis.

then volume
= [integral] pi(y^2)dx from -1 to 1
or
= 2pi[integral](x^2+1)^2 dx from 0 to 1
= 2pi[integral](x^4 + 2x^2 + 1) dx from 0 to 1

= ...
this is quite easy to integrate and finish.

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