Question

Generalize this to fine a formula for the integral:

sin(ax)cos(bx)dx

Could someone tell me what they got for an answer so I can check it to see if my answer is right.

My answer:
-1/2sinasinbx^2-1/3acosaxcosbx^3+ integral 1/3 a^2cosbx^3sinax..I'm not sure hot to find the integral of the last part.

Answer 1

I thnink the "generalizing" formula they expect you to use is the identity:

sin(ax) cos(by) = (1/2)[sin((a+b)x) + sin ((a-b)x)]

Those two terms can be easily integrated separately and added.