Question

integration of cos^23xfrom o to π/4

Answer 1

we know this identity:
cos 2x = 2cos^2 x - 1
rearranging, we will get cos^2 x = (cos2x + 1)/2.

now treat cos^2 3x as cos^2 x.
you will get cos^2 3x  =  (cos6x + 1)/2 =    (cos6x)/2 + 1/2.
integrating this you will get      (sin 6x)/12 + x/2;
now apply the limits
[sin(6 * $\pi$/4)/12 + pi/8]    -    [0+0]
                          = [sin(3 pi/2)/12 + pi/8]