Integration?

Question

pls guide me how to integrate this this absolute function
I(sin^3x)(cos^15x)I from 2pi to 0.
Thanks!

Answer 1

At first u should assume it is not absolute
so
sin^3x*cos^15x
=sinx*sin^2x*cos^15x
sinx*(1-cos^2x)*cos^15x
=sinx*cos^15x-sinxcos^17x
int=-cos^16x/16+cos^18x/18
now cuz it is absolute you should multiply the answer in
I(sin^3x)(cos^15x)I
/(sin^3x)(cos^15x)
and when it is 0/0 you should limit the answer
you should seperate integral to 4 part
0~pi/2
pi/2~pi
pi~3pi/2
3pi/2~2pi
Sorry for my English