Integral help? Second integral of a double integral?

The double integral is -pi/2 to pi/2, 0 to 2 cos(theta) of rcos(theta) r dr dtheta, but I'm stuck on the integral of 8/3 integral from -pi/2 to pi/2 of cos^3(theta) dtheta. help please?

2 Answers

  • 8 years ago
    Favorite Answer

    ∫ cos³(t) dt

    ∫ cos(t)cos²(t) dt

    ∫ cos(t)(1 - sin²(t)) dt

    ∫ cos(t) dt - ∫ sin²(t) dt

    u = sin(t)

    du = cos(t) dt

  • nle
    Lv 7
    8 years ago

    The inner integral is

    8/3 *integral cos^4(theta) d (theta)

    not cos^3

    The final answer is pi

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