Use the divergence theorem to evaluate the surface integral ∫∫S◯F⋅NdS where F=10xy^2zi+10yx^2zj+z^2k, S is the closed hemispherical surface z=√(1−x^2−y^2) together with the disk x^2+y^2≤1 in the xy-plane, and NN is the outward unit normal for S
Use the divergence theorem to evaluate the surface integral ∫∫S◯F⋅NdS where F=10xy^2zi+10yx^2zj+z^2k, S is the closed hemispherical surface z=√(1−x^2−y^2) together with the disk x^2+y^2≤1 in the xy-plane, and NN is the outward unit normal for S
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.3: Volume And Average Value
Problem 17E
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Use the divergence theorem to evaluate the surface integral ∫∫S◯F⋅NdS where F=10xy^2zi+10yx^2zj+z^2k, S is the closed hemispherical surface z=√(1−x^2−y^2) together with the disk x^2+y^2≤1 in the xy-plane, and NN is the outward unit normal for S
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