Find the area of the region common to the interiors of the cardioids r = 1+cospheta and r = 1-cospheta

Question

usukidoll · Answer

@zepdrix

zepdrix · Answer

Oh you chose to split it into 4 regions? :) that's clever hehe

usukidoll · Answer

yeah no way in hexland that I would write a lot of integrals

usukidoll · Answer

it was sort of easy to see which came first...the one with the minus sign.

usukidoll · Answer

does it look ok???

zepdrix · Answer

Mmm I'm having trouble getting through this one :(
I would have approached it differently.

Area of polar functions:$$\Large \frac{1}{2}\int\limits r^2\;d\theta$$

usukidoll · Answer

O_O

anonymous · Answer

That's what you get after one integration, so it shouldn't surprise anyone.

anonymous · Answer

Anyway, I'd say the lower limit of $r(\theta)$ should be $0$.

zepdrix · Answer

^

usukidoll · Answer

oh now I'm seeing this... more like r = 0 for the lower one and the r upper should be 1 because you need to solve for the r's or something like 1+cospheta=1-cospheta.

zepdrix · Answer

mm no the upper isn't 1.
See how the upper boundary of the radius is changing? it's the function r=1-cos theta.

anonymous · Answer

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