- #1
halfoflessthan5
- 16
- 0
what is the quick way of doing single integrals of the form:
*integral* (sinx)^n (cosx)^m dx
where n and m are just integers. These kind of integrals come up all the time in vector calculus and they take me ages to do. Is there a general method of doing them or a few common integrals i could learn? I end up having to apply about 3 trig identites and then sorting out the mess of resulting sinxs, cosx, cos2x etc
an eg would be
*integral* cosx (sinx)^2 dx
I would do this by using (sinx)^2 + (cosx)^2 = 1
then cos^2= 1/2(1 +cos2A)
then cosCcosD=1/2(cos(C+D) + cos(C-D))
Which takes about a side and a half of a4. There must be a simpler way (substitutions, change of variables?)
*integral* (sinx)^n (cosx)^m dx
where n and m are just integers. These kind of integrals come up all the time in vector calculus and they take me ages to do. Is there a general method of doing them or a few common integrals i could learn? I end up having to apply about 3 trig identites and then sorting out the mess of resulting sinxs, cosx, cos2x etc
an eg would be
*integral* cosx (sinx)^2 dx
I would do this by using (sinx)^2 + (cosx)^2 = 1
then cos^2= 1/2(1 +cos2A)
then cosCcosD=1/2(cos(C+D) + cos(C-D))
Which takes about a side and a half of a4. There must be a simpler way (substitutions, change of variables?)