Compute the integral of the vector field F(x, y, z) = (5x, 5y, 2z? ) over r(t) = (cos(t), sin(1). t) for 0 < 1 < a. (Use symbolic notation and fractions where needed.) F. dr =

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A: Please refer the attached image for complete solution.

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Q: 1. Determine whether F(x, y) et sin yi + e" cos syj is a conservative vector field.

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Q: Find the divergence of the vector field V(x, y, z) = −3xi + (y + 4 cos(x))j + (9z+ e5xy) k. (Give an…

A: Given that V(x, y, z) = −3xi + (y + 4 cos(x)) j + (9z + e^(5xy)) k.

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Q: [F. C F. dr =

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Q: Find the divergence of the vector field V(x, y, z) = −3xi + (y + 4 cos(x))j + (9z+exy) k. (Give an…

A: Given that V(x, y, z) = −3xi + (y + 4 cos(x)) j + (9z + e^(5xy)) k.