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: Integrate sinx*cox* using double angle

  1. Aug 5, 2013 #1
    1. The problem statement, all variables and given/known data

    ∫ Sinx cos x dx

    2. Relevant equations

    3. The attempt at a solution
    If you integrate it using substitution, you get -cos2(x)/2but if you use double angle formula to rewrite the problem, it will be ∫1/2 sin(2x), and integrate it, you get -cos(2x)/4. isn't it weird?
  2. jcsd
  3. Aug 5, 2013 #2
    You are forgetting that each of those two integrals must have ##+ C## appended to it. Now recall that ## \cos 2x = 2 \cos^2 x - 1 ##.
  4. Aug 5, 2013 #3

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    What voko said is exactly right. To elaborate, these two apparently different integrals differ only by a constant.
  5. Aug 5, 2013 #4
    So if I was to find the indefinite integral, both answers were right?
  6. Aug 5, 2013 #5
    None is correct unless you add the indefinite constant.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted