(See Steps) a) What do you mean when you say that a given vector field Field [x, y]=m[x, y], n[x, y] is a gradient field? b) The vector field field [x,
Question: a) What do you mean when you say that a given vector field Field \([x, y]=\{m[x, y], n[x, y]\}\) is a gradient field?
b) The vector field field \([x, y]=\left\{3 y^{2}+2,6 x y\right\}\) is a gradient field of some function f[x, y]. Find a function \(\mathrm{f}[\mathrm{x}, \mathrm{y}]\) whose gradient is field \([\mathrm{x}, \mathrm{y}]\) and explain how you found it.
Deliverable: Word Document 
(All Steps) Here are two curves: Given functions $m[x, y]$ and
![[See Solution] Consider the vector field Field](/images/solutions/MC-solution-library-71843.jpg "[See Solution] Consider the vector field Field [x, y]=m[x, y],")
[See Solution] Consider the vector field Field [x, y]=m[x, y],
[See Solution] Evaluate ∫_0^π ∫_y^π((Sin;[x])/(x))
(See Steps) Go with a given vector field \text Field [x, y]=3
Solution: Use the Gauss-Green formula to evaluate the path integral:
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