Help with this Definite Integral

[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

 

[arildno]

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

 

[chuachinghong]

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