find area inside the circle

Find the area of the region that is inside the circle r = 6cos(theta) but outside the cardoid r = 2 + 2cos(theta)

pic looks like this: http://us.st11.yimg.com/us.st.yimg.c...s_1932_3273205

needing help with this one please.

Hello, rcmango!

Quote:

Find the area of the region that is inside the circle: .r = 6·cosθ
but outside the cardoid: .r = 2 + 2·cosθ

Code:

| ** * | * * | * * * * | * *:::::* * | * *:::::* * |* *:::::* * | ::::: * * *:::::* - - - - - - - * - - - - - - *:::::* * * *:::::* * | :::::- * |* *:::::* * | * *:::::* * | * *:::::* * | * * * * | * ** |

Find the intersections of the two curves.

. . 6·cosθ .= .2 + 2·cosθ . → . 4·cosθ .= .2

. . cosθ .= .1/2 . → . θ .= .±π/3

Due to the symmetry, we can integrate from 0 to π/3 and multiply by 2.

A . = . 2 x (1/2) ∫ [(6·cosθ)² - (2 + 2·cosθ)²] dθ

Can you finish it now?

i'm not good at integrals, but i'm working on it. thankyou!

..still working on it.