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## Homework Statement

We are told to change the order of the given double integral. It is as follows:-

[tex]\int^{k}_{o}[/tex][tex]\int^{k+\sqrt{k^{2}-y^{2}}}_{-k+\sqrt{k^{2}-y^{2}}}[/tex] f(x,y)dxdy

## Homework Equations

The answer that I get after sketching the limits and finding the region is different from the answer given in my book. I would like to ascertain if its me who is wrong or the book(since the book has quite a lot of mistakes).

## The Attempt at a Solution

First I sketched the given limits, and I got the upper half of the two given circles since y=0 is also a limit. Then I got a region bounded by the limits. Since it is kinda hard to describe, I am just writing the answer that I am getting after changing the order. It is as follows:-

[tex]\int^{0}_{-k}[/tex][tex]\int^{k}_{\sqrt{k^{2}-(x+k)^{2}}}[/tex] f(x,y)dydx + [tex]\int^{k}_{0}[/tex][tex]\int^{k}_{\sqrt{k^{2}-(x-k)^{2}}}[/tex] f(x,y)dydx

But the answer given in my textbook has three parts, thereby indicating that the region I got is wrong.

Any help pointing me in the right direction would be helpful.