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!

Simple derivative problem

  1. Feb 4, 2004 #1
    I am taking basic calculus, and have just got to integration. Can someone please tell me how to find the antiderivative of (sin(x))^4?
  2. jcsd
  3. Feb 4, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Looks like home work. Replace a power with a multiple - you can do sin^2 using cos 2, so this is no harder.
  4. Feb 4, 2004 #3
    Sorry, but I still don't understand. How do you find the antiderivative of (sin(x))^2? Could you explain it to me please?
  5. Feb 4, 2004 #4


    User Avatar
    Science Advisor
    Homework Helper

    Do you know about the chain rule?
    do you know the derivatives of [tex]\sin x[/tex] and [tex]x^2[/tex]?
  6. Feb 5, 2004 #5
    Yes, but how are they going to help me find the antiderivative of [tex]sin^4x[/tex]?
  7. Feb 5, 2004 #6
    Try to Reduce the power of sin4x by


    i.e 1+cos22x-2cos2x
    Again use

    2cos22x = 1+cos24x

    Simplifying u will obtain

    [tex]\sin^4x = \frac{3}{8} +\frac{cos4x}{8}-\frac{cos2x}{2}[/tex]

    Hope this will help u
  8. Feb 5, 2004 #7


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member


    I think you have a typo

    Should be

  9. Feb 5, 2004 #8
    Ya typo is there it is

    2cos22x = 1+cos4x

    error is regretted
  10. Feb 5, 2004 #9

    Thanks a lot, I understand now.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook