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Math Help - Integration of powers of sin and cosine.

  1. #1
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    Integration of powers of sin and cosine.

    I suspect this is a simple problem and I'm just missing something obvious ... but I can't seem to figure it out. Here it is:

    Integrate: sin^4(x/2) * cos (x/2)

    I'm aware that the sine function is to an even power and cosine to an odd, and normally you'd use the substitution u=sinx in this case. It's the x/2 part that's throwing me off here. Any help appreciated, thank you.
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  2. #2
    Super Member Quacky's Avatar
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    So just let u=Sin(\frac{x}{2})

    Then du=\frac{1}{2} Cos(\frac{x}{2}) dx, and go through from there as normal with the substitution.

    Alternatively, use the rule that \int f'(x)[f(x)]^n dx=\frac{f(x)^{n+1}}{n+1}+C and manipulate slightly.
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  3. #3
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    ^ Ah of course, staring me in the face the whole time... many thanks pal!
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