# Multivariable Calculus : Double Integral - The Polar Coordinates

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Solve by double integration in polar coordinates: Find the volume bounded by the paraboloids z = x^2 + y^2 and z = 4 - 3x^2 - 3y^2

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##### Solution Summary

A double integral is calculated.

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We define

x=rcos(theta)

y=rsin(theta)

z=r

then the jacobian would be r. We must find

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