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## Homework Statement

Express [itex]f(x,y) = \frac{1}{\sqrt{x^{2} + y^{2}}}\frac{y}{\sqrt{x^{2} + y^{2}}}e^{-2\sqrt{x^2 + y^2}}[/itex] in terms of the polar coordinates [itex]\rho[/itex] and [itex]\phi[/itex] and then evaluate the integral of [itex]f(x,y)[/itex] over a circle of radius 1 centered at the origin.

## Homework Equations

[itex]y = \rho \sin(\phi)[/itex]

[itex]\rho = \sqrt{x^{2} + y^{2}}[/itex]

## The Attempt at a Solution

Using the above relevant equations;

[itex]f(\rho,\phi) = \frac{\sin(\phi)}{\rho}e^{-2\rho}[/itex].

I am confused about what the second half of this question is asking me to do. The integral of a function gives the area under the curve, so surely evaluating an integral over a circle, merely gives the area of the circle?

It also looks like it would make more sense to evaluate the integral of [itex]f(\rho,\phi)[/itex] than [itex]f(x,y)[/itex].

EDIT - I just had a rather obvious thought. This is akin to asking me to find the mass of a circle, with density given by the function... If that's correct, then I think i'm ok.

EDIT2 - Also, with regards to performing the integral of [itex]f(x,y)[/itex] the fact that it is a circle radius 1 means that [itex]\sqrt{x^2 + y^2} = 1[/itex], right? So that makes my job much easier.

I'd appreciate some guidance about what this question is asking of me.

Thanks.

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