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Math

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Express sin^6theta in multiples of costheta and hence evaluate the integral of sin^6theta from 0 to pi/2.

Thanks in advance! :)

  • Math -

    sin^6θ = (sin^2θ)^3
    = (1 - cos^2θ)^3
    = 1 - 3cos^2θ + 3cos^4θ + cos^6θ

    Now you can use your half-angle formula

    cos^2θ = (1 + cos 2θ)/2

    to get no exponents and multiples of θ.

    You will end up with

    1/192 (60θ - 45sin2θ + 9sin4θ - sin6θ)

    from 0 to pi/2 yields 30pi/192

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