# Multivariable Calculus : Double Integral - Polar Coordinate

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( âˆ« ^n_r means that n is on the top of the âˆ« and r is on the bottom) Evaluate the given integral by first converting to polar coordinates:

âˆ« ^2_1 âˆ« ^(square root of 2x - x^2)_0 (1/(square root of x^2 + y^2)) dy dx

âˆ«: is the integral symbol

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#### Solution Preview

I show the same integral like this:

int(int(1/(sqrt(x^2+y^2),y=sqrt(2x-x^2)..0),x=1..2)

First we must solve

int(1/(sqrt(x^2+y^2),y=sqrt(2x-x^2)..0) and of course we must ...

#### Solution Summary

A double integral is solved. The polar coordinates are analyzed.

$2.49