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## adeniyta 2 years ago 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.

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1. adeniyta

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

2. NoelGreco

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.

3. adeniyta

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

4. adeniyta

I got 4/e for answer.

5. adeniyta

It was right- hallelujah! Thanks!

6. NoelGreco

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

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