How do I deal with the coefficient in the argument of the following problem? Integrate: e^(cost)*sin(2t)dt from 0 to pi
I am not sure how to do substitution with this. I made u= cost du= -sintdt and then I integrated and multiplied the end points by two to get e-e^-1. I retyped the problem in below space.

Question

anonymous · Answer

$$\int\limits_{0}^{\pi}e ^{cost}\sin2tdt$$

noelgreco · Answer

Your problem is the 2.  Use the double angle trig identity:

$$\sin (2x) = 2\sin x \cos x$$

Then do your u substitution using u = cos x.

Integrate by parts, and enjoy.

anonymous · Answer

Okay, thank you. This was very helpful, have a good day!:)

anonymous · Answer

I got 4/e for answer.

anonymous · Answer

It was right- hallelujah! Thanks!

noelgreco · Answer

You bet.  We take precalculus for a reason, no?