If you attempt to use Formula 2 to find the area of the top half of the

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If you attempt to use Formula 2 to find the area of the top half of the sphere x2 + y2 + z2 = a2, you have a slight problem because the double integral is improper. In fact, the integrand has an infinite discontinuity at every point of the boundary circle x2 + y2 = a2. However, the integral can be computed as the limit of the integral over the disk x2 + y2 < t2 as t→ a-. Use this method to show that the area of a sphere of radius a is 4πa2.

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