# Area Between Two circles

xdrgnh

## Homework Equations

equation of each circle (x-2)^2+y^2=9
(x+2)^2+y^2=9

## The Attempt at a Solution

I solve for y for the circle (x-2)^2+y^2=9 then I took the integral of that from -1 to 0. I noticed that the shape looked symmetrical so I multiplied it by 4. But when I do it algebraically and using geometry I get a different answer then when I use the calculus.

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Homework Helper
Nobody can say why you are getting different answers until you show how you did it and what you got.

xdrgnh
Nobody can say why you are getting different answers until you show how you did it and what you got.

Well I really didn't do it algebraically the internet told me how to do it algebraically and it wasn't the same answer I got with my calculus. So the integral of one of the circles is .5(9arcsin(x-2)/3)+(x-2)(9-(x-2)^2)^.5) the limits are from -1 to 0. So I evaluated it and I got 1.584, something around there. And you see the shape is symmetrical on the link I put in. So I mult it by 4 but that did not give the right answer according to the internet. Did I do it the right way.

Homework Helper
I get something about like that for one fourth of the region. 1.548. I think you are probably right. What's the 'internets' answer?

xdrgnh
Ok, so what did you put in for the angle? It's likely not the same as in that problem.

I just did the same thing they did except using a my radius of 3 instead of 10. Do you think that my answer is right and maybe what they are doing just doesn't apply in my case. The problem is supposed to be solved using calculus not geometry.