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# Help with a Maths question? watch

1. By converting to plane polar co-ordinates r,theta , evaluate ∫∫ y^2/x^2 dA; where R is the finite region in the x,y plane between the circles (x− 6)^2 + y^2 = 36 and (x − 7)^2 + y^2 = 49; and below the line y = x.

The trouble I am having is trying to work out the limits. The limits i got for r was 12cos(theta) then 14cos(theta). I don't know if that is right and how to get the limits for theta. Can anyone help me?

Thank You very much in advance !!!!!!
2. I think your limits for are correct.

From sketching it, I believe the limits for should be (corresponding to the lower limit) to (corresponding to the line y = x).

Hence your integral is something like:

I'm quite rusty, so don't take anything I say as gospel.

I performed this integral and got:

3. (Original post by Kerch)
I think your limits for are correct.

From sketching it, I believe the limits for should be (corresponding to the lower limit) to (corresponding to the line y = x).

Hence your integral is something like:

I'm quite rusty, so don't take anything I say as gospel.

I performed this integral and got:

You probably are right Thanks.

Just one thing I don't get though is how do you get - pi/2 for the lower limit of theta?
4. (Original post by ihatebrownbread)
You probably are right Thanks.

Just one thing I don't get though is how do you get - pi/2 for the lower limit of theta?
Not sure how to express it mathematically, but if you sketch it you see the bounding curves that form the circles meet the y axis at a tangent and all the area is contained in the positive x area of the plane.

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