## anonymous 5 years ago find a formula for the area inside the cardoid r=a+acos(thetat), a>0

1. anonymous

a cardoid is a circle with a little pinched thingy like a navel

2. anonymous

No thats an annulus. A cardioid is given by that function. The best way to solve this would be to integrate by polar coordinates. Do you know how to do that?

3. anonymous

$\int\limits_{0}^{2\pi}\int\limits_{0}^{a + acos(\theta)}rdrd \theta$

4. anonymous

5. anonymous

...what's the expression inside cos( ? Is it r = a + a * cos(theta * t)?

6. anonymous

davismj, usually what you'd do to find the area inside a polar curve, r, is to do one integration. In standard form: $\frac{1}{2} \int\limits \ r^2 d\theta$ from the area of a circular sector, with infinitesimally small angles.

7. anonymous

Your integral is equivalent to mine.

8. anonymous

Exactly, it's just that it seems like the OP's type of problem is usually solved with a simpler form of the integral. Just wanted to point it out, in case he/she hasn't seen multiple integrals yet.

9. anonymous

Good point.