I am supposed to find the area of the region given two boundaries and two functions revolving about the x axis.

Question

x = 0
x = pi/2

y = cos(x/2)
y = sin(x/2)

Graphing those two functions made me select to use the washer method.
Therefore, I set my definite integral to this:

pi∫[0,pi/2] cos^2(x/2) - sin^2(x/2) dx

Is that the correct way of setting up the definite integral? I can integrate easily, but it's always setting it up is the most difficult part. Any help is greatly appreciated!

Answer 1

looks good to me