# Help with this Definite Integral

1. Sep 29, 2006

### chuachinghong

Well as I am practising for my coming test, I encountered this question:

Integrate
f(x) = absolute [(sin X)^3 * (cos X)^15]dx
within the interval of [0,2pi]

I tried simplifying this integral into...

f(x) = absolute[ ((cos X)^15)*(sin X) -((cos X)^17)*(sin X))] dx
within the interval of [0,2pi]

Also, I break up the integral into 4 parts of pi/2 each i.e [0,pi/2], [pi/2,pi], [pi,3pi/2] and [3pi/2, 2pi]

My question is, when I am calculating the interval of the Second Quadrant, which is from [pi/2, pi]. What should my f(x) look like after taking out the absolute sign?

Hope you can help me with this. Thank you

Last edited: Sep 29, 2006
2. Sep 29, 2006

### arildno

sine is positive, cosine is negative in the second quadrant, and your powers are odd, so...?

3. Sep 29, 2006

### chuachinghong

Oh ok I got it. Thanks for your help. @,@