Use the method of cylindrical shells to find the volume generated by rotation the region bounded by the given curves about the specified axis.
y = x^2, y = 2-x^2; about x = 1
The Attempt at a Solution
I tried to just break it down.
I want something of the form 2∏rhΔr
OK so To find the height f(x) I subtracted.
2-x^2-x^2 = 2-2x^2. For the radius I did a-x so 1-x is the radius
So I have
V = 2∏∫ (1-x)(2-2x^2)dx between -1 and 1 because that is where the graphs intersect.
Evaluating it I got 2∏((x^4)/2 -(2x^3)/3 -x^2 +2x ] between -1 and 1
I got 16∏/3
Is this the right way?