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!

Finding the indefinite integral of sin^2(pi*x) cos^5(pi*x)

  1. Feb 19, 2016 #1
    1. The problem statement, all variables and given/known data
    ∫(sin2(πx)*cos5(πx))dx.

    2. Relevant equations
    Just the above.

    3. The attempt at a solution
    I have no idea how pi effects the answer, so I basically solved ∫(sin2(x)^cos5(x))dx.

    ∫(sin2(x)*cos4(x)*cos(x))dx
    ∫sin2(x)*(1-sin2(x))2*cos(x))dx
    U-substitution
    u = sin x du = -cos x dx

    ∫(u2*(1-u2)2) -du
    -∫(u2*(1-u2)2) du
    -∫(u2*(1-2u2+u4) du
    -∫(u2-2u4+u6) du

    -((u3/3)-(2u5/5)+(u7/7).

    When I look up what the antiderivative should be on integral-calculator.com. the minus sign outside of the parentheses disappears, which I can't figure out how.

    Can anyone give me some help?
     
  2. jcsd
  3. Feb 19, 2016 #2

    RUber

    User Avatar
    Homework Helper

    If u = sin x then du = cos x, not - cos x.
     
  4. Feb 19, 2016 #3

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Fix the sign error that RUber pointed out. Then do the original problem the same way but let ##u =\sin(\pi x)##.
    [Edit:] Fixed typo.
     
    Last edited: Feb 19, 2016
  5. Feb 19, 2016 #4

    Mark44

    Staff: Mentor

    No doubt just an oversight, but du = cos(x) dx.
     
  6. Feb 29, 2016 #5
    Thanks everyone. Figured it out.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Finding the indefinite integral of sin^2(pi*x) cos^5(pi*x)
Loading...