Any part of the surface of a sphere can identified as S = {(r, , )|r = R, 2 [min, max] , 2 [min, max]]. Let F(r, , ) = Fr(r, , ) ar + F(r, , ) a + F(r, , ) a be a vector function.

(i) Make a program to calculate the surface integral S F dA. Note that this program must be general to accept diverse inputs and deliver an output.

(ii) For D = 3 cos sin ar + 4.5 sin cos a C m2, R = 3 102 m, min = 0, max = /2, min = /4, and max = 3/8, use your program to determine S D dA

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