Calculus

PLEASE HELP! Which one or ones of the following integrals produces the area that lies inside the circle r = 3 sin θ and outside the cardioid r = 1 + sin θ? (10 points)

I. one half times the integral from pi over 6 to 5 times pi over 6 of the quantity 9 times the sine squared of theta minus the square of 1 plus sine theta, d theta
II. the integral from pi over 6 to pi over 2 of the quantity 9 times the sine squared of theta minus the square of 1 plus sine theta, d theta
III. one half times the integral from 0 to pi over 6 of the quantity 9 times the sine squared of theta minus the square of 1 plus sine theta, d theta plus one half times the integral from 5 times pi over 6 to pi of the quantity 9 times the sine squared of theta minus the square of 1 plus sine theta, d theta

A) I only
B) I and II only
C) II only
D) III only

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  1. yes

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  2. You are correct Aria.

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  3. WHICH ONE IS IT. I am a little confused.

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  4. If you have
    R = 3 sinθ
    r = 1 + sin θ
    then you want A = ∫1/2 (R^2-r^2) dθ

    Sorry, I just can't see wading through all those words to see which matches.

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    oobleck

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