find a formula for the area inside the cardoid r=a+acos(thetat), a0

Question

find a formula for the area inside the cardoid r=a+acos(thetat), a>0

anonymous · Answer

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

anonymous · Answer

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?

anonymous · Answer

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

anonymous · Answer

Watch your language on this site, talking about annulus.

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

Your integral is equivalent to mine.

anonymous · Answer

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.

anonymous · Answer

Good point.