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10. Set up a double integral to find the volume under f(x, y) = x²+y2 ≤9,x≥0. Do not integrate. In(x²+y²) √√x²+y2 on the region 11. Given the vector field F(x, y, z) = yz cosxî+ (2y + z sinx)ĵ + (y sin x - 1)k, find the potential function if it exists; if not, explain why not.

10. Set up a double integral to find the volume under f(x, y) = x²+y2 ≤9,x≥0. Do not integrate. In(x²+y²) √√x²+y2 on the region 11. Given the vector field F(x, y, z) = yz cosxî+ (2y + z sinx)ĵ + (y sin x - 1)k, find the potential function if it exists; if not, explain why not.

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 12E
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10. Set up a double integral to find the volume under f(x, y) = x²+y2 ≤9,x≥0. Do not integrate. In(x²+y²) √√x²+y2 on the region 11. Given the vector field F(x, y, z) = yz cosxî+ (2y + z sinx)ĵ + (y sin x - 1)k, find the potential function if it exists; if not, explain why not.
Transcribed Image Text:10. Set up a double integral to find the volume under f(x, y) = x²+y2 ≤9,x≥0. Do not integrate. In(x²+y²) √√x²+y2 on the region 11. Given the vector field F(x, y, z) = yz cosxî+ (2y + z sinx)ĵ + (y sin x - 1)k, find the potential function if it exists; if not, explain why not.
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