this is my question, any help would be appreciated. Consider the vector D=3sin( theta) ar (unit vector).

Mehlqv 2022-08-13 Answered
Consider the vector D = 3 sin ( θ ) ar (unit vector).
Evaluate the integral
S D   d S ,
where S is the surface of a sphere with radius r=5 centered at the origin.
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Answers (1)

Donovan Shields
Answered 2022-08-14 Author has 13 answers
In terms of polar coordinates, the surface area element at constant r, in your case r=5, is r 2 sin θ d θ d ϕ. Let n ^ denote the unit vector parallel to, D so your integral is
0 2 π d ϕ 0 π d θ r 2 sin θ D n ^ = 150 π 0 π sin 2 θ d θ = 75 π 2 .
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