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: How to integrate this

  1. Feb 3, 2013 #1
    [tex]\displaystyle\int sin^22tcos^2t\ dt [/tex]

    This was part (b) to a question, the previous part of the question was to integrate [itex] \displaystyle\int sin^22tcost\ dt [/itex] which I managed to do by expressing [itex] sin^22t [/itex] as [itex] 4(sin^2t - sin^4t) [/itex]

    I tried a similar method for the integrand above, but didn't really go far with it. I'm not really sure what I'm trying to spot here, and I usually struggle with these integrals.
  2. jcsd
  3. Feb 3, 2013 #2
    You can try with [itex]\int sin^2(2t)dt - \int sin^2(2t)sin^2(t)dt[/itex], plus some trigonometric manipulations.

    P.S.: Silly me, perhaps you only need some trigonometric manipulations.
  4. Feb 3, 2013 #3
  5. Feb 3, 2013 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Instead of changing the first factor, I'd use the identity ##\cos^2 t = \frac{1+\cos 2t}{2}## to get everything in terms of ##2t##. It should be pretty straightforward after that.

    Your original approach would also work. You should check your textbook on how to handle integrals of the form
    $$\int \cos^n x \sin^m x\,dx.$$ They're tedious, but there's a recipe to follow that depends on the evenness and oddness of ##m## and ##n##.
  6. Feb 3, 2013 #5


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    After following vela's advice, you may also find it useful to know cos(3x) = 4 cos3(x) - 3 cos(x)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook