Question

what would your bounds be if you were looking for the area of the polar function r=2+4cosx but not including the small loop. the picture is in this link: http://tutorial.math.lamar.edu/Classes/CalcII/PolarArea.aspx

Example 1

Answer 1

The bigger one is a specific shape, I forgot the name, it is given as a question or problem all the time. I don't know if the cos thing is different from that one given, but it has its own name and cosine thingy.

Answer 2

right, but if you were looking for the total area of that, what would be the bounds of the integral?

Answer 3

It would have something that looks just like the other one. Let me find. One guy was here the other day asking tons of questions about it.

Answer 4

i think it could be from 0 to 2pi/3

Answer 5

It's called a cardioid r=a(1-costheta)

Answer 6

yes, thank you. Do you agree with my proposed bounds?

Answer 7

In double integrals, I think it goes 0 to 2 pi. But it is such a familiar shape (I think its in medical, it looks like an eyeball) it is easily done in single integral. The integral of (1/2) r^2 dtheta

Answer 8

Now the info I gave you was for the cardioid without the inner loop. With it, a different approach.