The Surface Area formula for Parametric Surfaces // Vector Calculus
In this video we derive the formula to compute surface area given some surface described parametrically. Thus if you have a parametric description, all you need to do is plug it into this formula. The derivation works by looking at a tiny section of surface area, and approximating this with a little tangential parallelogram whose area can be computed by the length of the cross product of r_u Delta u and r_v Delta b, the partial derivatives of the position vector with respect to the two parameters u and v. Thus the integral is effectively just summing up these little surface areas and becomes a double integral of the length of that cross product. We will see a concrete example of this in the next video in the vector calculus playlit.
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