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bthomas872

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The question states, If a is a positive number, what is the value of the following double integral?

integral from 0 to 2a [ integral from - sqrt(2ay - y^2) to 0 of sqrt(x^2 + y^2) dy dx.

My first thought is that we should change to polar coordinates so I do not have to do a trigonometric substitution.

So then it would sqrt(r^2) r dr d(theta) which would simplify to r^2 dr d(theta).

What i am confused with is now how to change my limits of integration to polar? Can someone help please.

integral from 0 to 2a [ integral from - sqrt(2ay - y^2) to 0 of sqrt(x^2 + y^2) dy dx.

My first thought is that we should change to polar coordinates so I do not have to do a trigonometric substitution.

So then it would sqrt(r^2) r dr d(theta) which would simplify to r^2 dr d(theta).

What i am confused with is now how to change my limits of integration to polar? Can someone help please.

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