anonymous
  • anonymous
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.
MIT 18.01 Single Variable Calculus (OCW)
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\int\limits_{0}^{\pi}e ^{cost}\sin2tdt\]
NoelGreco
  • 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.
anonymous
  • anonymous
Okay, thank you. This was very helpful, have a good day!:)

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anonymous
  • anonymous
I got 4/e for answer.
anonymous
  • anonymous
It was right- hallelujah! Thanks!
NoelGreco
  • NoelGreco
You bet. We take precalculus for a reason, no?

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