Calc check find the volume generated by revolving the curve y=cos 3x about the x axis, 0<=x<=pi/36?

Question

My solution is pi^2/72 + pi/36

Answer 1

pi*integral cos^2(3x) dx
cos^2x= (cos2x+1)/2
cos^2(3x)=(cos6x+1)/2
therefore:
pi* integral (cos6x)/2 +1/2 dx
=pi[(sin6x)/12 -x/2] 0-pi/36
= pi[{sin(pi/6)/12 +pi/72}-0
= pi*(1/24) +pi^2/72
=pi/24 +pi^2/72

Answer 2

I've done this rather quickly so may have made a slip but I get pi^2/72 + pi/24