Multivariable Calculus (Calc III) - Complete Semester Course - Surface Integrals: Why 'r' Isn't Needed When Parametrizing with Polar Coordinates

Let's address a common misconception when computing surface integrals for parametrized surfaces. Typically, when integrating in polar coordinates, 'r' is a necessary factor in the differential, like 'r dr dθ'. However, with surface integrals, the parametrization of the surface itself inherently accounts for any such scaling! I demonstrate this by comparing a standard double integral in polar coordinates to a surface integral computation. (The integrals themselves are not too exciting and could be done with basic geometry.) #mathematics #math #multivariablecalculus #doubleintegrals #polarcoordinates #surfaceintegral