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Homework Help: Trigonometric Integrals

  1. Jun 13, 2010 #1
    1. The problem statement, all variables and given/known data

    integral 31(cos^2x)(sin(2x)dx

    2. Relevant equations



    3. The attempt at a solution
    I am so lost on this problem... Any suggestions would be great
     
  2. jcsd
  3. Jun 13, 2010 #2

    phyzguy

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    Try looking up the double angle identities and use them to re-write sin(2x). Then try integration by substitution.
     
  4. Jun 13, 2010 #3
    So if the double angle for sin(2x) is 2sinxcosx... the problem would be rewritten as integral 31cos^2x(2sinxcosx)dx? Then what??? Sorry im still confused

    Thanks for the help!
     
  5. Jun 13, 2010 #4

    phyzguy

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    Now collect the cos(x) terms together. Then what do you have?
     
  6. Jun 13, 2010 #5
    So it would become integral 31(2sinxcos^3)... Then make u=sinx du=cosxdx... Which would lead to 31 integral 2sinxcos^2xcosxdx... Then 31 integral 2sinx(1-sin^2x)du... 31 integral 2u(1-u^2)du... Eventually leading to 31u^2-31/2u^4... And then 31sin^2x-31/2sin^4x.. How does that look??
     
  7. Jun 13, 2010 #6

    phyzguy

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    It's much simpler if you try u=cos(x), but I think your solution is correct.
     
    Last edited: Jun 13, 2010
  8. Jun 13, 2010 #7
    Awesome! Thank you so much. I have another question if you don't mind.. . For Integral 3x(cos(2x))^2dx could I use u substitution with the 3x
     
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