Question
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.
1. y= x squared + 2, x = negative 1, x = 1 about y = 1.
Answers
Reiny
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.
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.