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Use the divergence theorem to write a triple integral that is equivalent to the flux integral - = 64 and F(x, y, z) = 4x²y² i +8x³yj — 4x²y³k and S is the surface of the solid E bounded by the cylinder x² + y² the planes z = 0 and z = y + 6. Do not evaluate the integral. Hint: convert to cylindrical coordinates and ensure all limits of integration are non-negative. Provide your answer below: SSF - ds = 12280) F.ds, where dz dr de

Use the divergence theorem to write a triple integral that is equivalent to the flux integral - = 64 and F(x, y, z) = 4x²y² i +8x³yj — 4x²y³k and S is the surface of the solid E bounded by the cylinder x² + y² the planes z = 0 and z = y + 6. Do not evaluate the integral. Hint: convert to cylindrical coordinates and ensure all limits of integration are non-negative. Provide your answer below: SSF - ds = 12280) F.ds, where dz dr de

Calculus For The Life Sciences
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 19E
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Use the divergence theorem to write a triple integral that is equivalent to the flux integral + [/Ⓡ F(x, y, z) = 4x²y² i +8x³yj − 4x²y³ k and S is the surface of the solid E bounded by the cylinder x² + y² = 64 and the planes z = 0 and z = y + 6. Do not evaluate the integral. Hint: convert to cylindrical coordinates and ensure all limits of integration are non-negative. Provide your answer below: 8880 SSF · ds = √ F.ds, where dz dr de
Transcribed Image Text:Use the divergence theorem to write a triple integral that is equivalent to the flux integral + [/Ⓡ F(x, y, z) = 4x²y² i +8x³yj − 4x²y³ k and S is the surface of the solid E bounded by the cylinder x² + y² = 64 and the planes z = 0 and z = y + 6. Do not evaluate the integral. Hint: convert to cylindrical coordinates and ensure all limits of integration are non-negative. Provide your answer below: 8880 SSF · ds = √ F.ds, where dz dr de
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