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
4 answers
yes
You are correct Aria.
WHICH ONE IS IT. I am a little confused.
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.
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.
1 answer