$\"\"$

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Change of variable in double integral :

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$\"\"$

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Conversion of integral from rectangular to polar co-ordinates : $\"\"$

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$\"\"$

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The integral is $\"\"$ and the change of variables $\"\"$ .

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Where R is the region bounded by the ellipse $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in above equation.

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$\"\"$

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Since the domain is a unit circle, the limits of integral are $\"\"$ and .

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$\"\"$

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Find the Jacobian :

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$\"\"$

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$\"\"$

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Evaluate the integral :

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$\"\"$

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Write the integral in polar co-ordinates :

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Substitute $\"\"$ and $\"\"$ .

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Since the domain is a unit circle, the new limits are $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$