1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor

    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

    User Avatar
    Science Advisor

    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

    User Avatar
    Science Advisor

    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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook