(See Solution) Go with a given vector field \text Field [x, y]=3 x^2 y^4, 4 x^3 y^3 with the extra information that Field [x, y] is a gradient field. Here's

Question: Go with a given vector field

\[\text { Field }[x, y]=\left\{3 x^{2} y^{4}, 4 x^{3} y^{3}\right\}\]

with the extra information that Field [x, y] is a gradient field. Here's a closed curve C:

For this curve, what is the value of

$\int_{\mathrm{C}} \mathrm{m}[\mathrm{x}, \mathrm{y}] d \mathrm{x}+\mathrm{n}[\mathrm{x}, \mathrm{y}] d \mathrm{y} ?$ Explain.

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(See Solution) Go with a given vector field \text Field [x, y]=3 x^2 y^4, 4 x^3 y^3 with the extra information that Field [x, y] is a gradient field. Here's

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