Table 9.6.2(a) provides a solution via task template.
Tools≻Tasks≻Browse
Calculus - Vector≻Integration≻Surface Integration≻Over a Sphere
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Surface Integral on a Sphere
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Integrand
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Sphere Radius:
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Table 9.6.2(a) Solution via task template
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If the sphere is parametrized by the equations
then the task-template solution in Table 9.6.2(b) is available. Note that and .
Tools≻Tasks≻Browse
Calculus - Vector≻Integration≻Surface Integration≻Over a Parametrically Defined Surface
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Surface Integral on a Surface Defined Parametrically
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Integrand
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Table 9.6.2(b) Alternate solution by task template
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A final simplification sets , the complex sign of , to 1 since .