Let H be the hemisphere x 2 + y 2 + z 2 = 50, z >

Question:

Let H be the hemisphere x² + y² + z² = 50, z > 0, and suppose f is a continuous function with f (3, 4, 5) = 7, f (3, -4, 5) = 8, f (-3, 4, 5) = 9, and f (-3, -4, 5) = 12.
By dividing H into four patches, estimate the value of ʃʃ_H f(x, y, z) dS.

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