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Help with this Definite Integral

  1. Sep 29, 2006 #1
    Well as I am practising for my coming test, I encountered this question:

    f(x) = absolute [(sin X)^3 * (cos X)^15]dx
    within the interval of [0,2pi]

    I tried simplifying this integral into...

    f(x) = absolute[ ((cos X)^15)*(sin X) -((cos X)^17)*(sin X))] dx
    within the interval of [0,2pi]

    Also, I break up the integral into 4 parts of pi/2 each i.e [0,pi/2], [pi/2,pi], [pi,3pi/2] and [3pi/2, 2pi]

    My question is, when I am calculating the interval of the Second Quadrant, which is from [pi/2, pi]. What should my f(x) look like after taking out the absolute sign?

    Hope you can help me with this. Thank you :smile:
    Last edited: Sep 29, 2006
  2. jcsd
  3. Sep 29, 2006 #2


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    sine is positive, cosine is negative in the second quadrant, and your powers are odd, so...?
  4. Sep 29, 2006 #3
    Oh ok I got it. Thanks for your help. @,@
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