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adeniyta Group Title

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.

  • 2 years ago
  • 2 years ago

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  1. adeniyta Group Title
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    \[\int\limits_{0}^{\pi}e ^{cost}\sin2tdt\]

    • 2 years ago
  2. NoelGreco Group Title
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    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.

    • 2 years ago
  3. adeniyta Group Title
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    Okay, thank you. This was very helpful, have a good day!:)

    • 2 years ago
  4. adeniyta Group Title
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    I got 4/e for answer.

    • 2 years ago
  5. adeniyta Group Title
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    It was right- hallelujah! Thanks!

    • 2 years ago
  6. NoelGreco Group Title
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    You bet. We take precalculus for a reason, no?

    • 2 years ago
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