How do you find the volume of y = 11sinx , y=0, [ 0,pi ] revolving about the x axis?

1 Answer
Jun 10, 2015

V=121/2pi^2~~597.111.

Explanation:

This is the formula for calculating the volume of a solid obtained from a revolution around the x-axis:
V=pi*int_a^b f^2(x) dx
Our function f(x)=11sinx and a=0, b=pi.
So the volume is:
V=pi*int_0^pi 121sin^2(x) dx
V=121pi*int_0^pi sin^2(x) dx
V=121pi*[1/2(x-sin(x)cos(x))]_0^pi=121/2pi[x-sin(x)cos(x)]_0^pi
V=121/2pi(pi-0-0+0)=121/2pi^2~~597.111.
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