Surface integrals using a parametric description Evaluate the surface integral ∫∫S ƒ dS using a parametric description of the surface. ƒ(x, y, z) = x2 + y2, where S is the hemisphere x2 + y2 + z2 = 36, for z ≥ 0
Surface integrals using a parametric description Evaluate the surface integral ∫∫S ƒ dS using a parametric description of the surface. ƒ(x, y, z) = x2 + y2, where S is the hemisphere x2 + y2 + z2 = 36, for z ≥ 0
Surface integrals using a parametric description Evaluate the surface integral ∫∫S ƒ dS using a parametric description of the surface. ƒ(x, y, z) = x2 + y2, where S is the hemisphere x2 + y2 + z2 = 36, for z ≥ 0
Surface integrals using a parametric descriptionEvaluate the surface integral∫∫SƒdSusing a parametric description of the surface.
ƒ(x, y, z) = x2 + y2, where S is the hemisphere x2 + y2 + z2 = 36, for z ≥ 0
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Expert Solution
Step 1
Given: To find: using a parametric description of the surface.
Step 2
We have,
Use the spherical coordinate with .
Parametrizing the given curve, we get
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