calculus

Use the Table of Integrals to evaluate the integral.

0 to π ∫cos^6(θ) dθ
I don't see anything like that on the table of integral. Need some help.

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  1. Yeah, you probably won't find 6th powers of trig functions in the table. Many go up to 4 or 5. What you have to rely on here is the double angle formulas to lower the power.

    cos2x = 2cos^2x - 1
    so, cos^2x = (1+cos2x)/2
    so, cos^6x = (cos^2x)^3 = ((1+cos2x)/2)^3
    = 1/8 (1+3cos(2x)+3cos^2(2x) + cos^3(2x))
    You can probably find powers 1,2,3 of cos(x) in your table.

    when you're all done, you can check your work with any of many handy integral calculors, such as wolframalpha.com

    Just type in your integral

    integral[0..pi] cos^6(θ) dθ

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    posted by oobleck

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