Let $\vec{F}=\left(y^{2}+y \sin (x y)\right) \vec{i}+(4 x y-y+x \sin (x y)) \vec{j}$ Is $\vec{F}$ path-independent?

Name: Let $\vec{F}=\left(y^{2}+y \sin (x y)\right) \vec{i}+(4 x y-y+x \sin (x y)) \vec{j}$ Is $\vec{F}$ path-independent?
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The Answer of Let $\vec{F}=\left(y^{2}+y \sin (x y)\right) \vec{i}+(4 x y-y+x \sin (x y)) \vec{j}$ Is $\vec{F}$ path-independent?

Let F⃗=(y2+ysin⁡(xy))i⃗+(4xy−y+xsin⁡(xy))j⃗\vec{F}=\left(y^{2}+y \sin (x y)\right) \vec{i}+(4 x y-y+x \sin (x y)) \vec{j}F=(y2+ysin(xy))i+(4xy−y+xsin(xy))j​

Let $\vec{F}=\left(y^{2}+y \sin (x y)\right) \vec{i}+(4 x y-y+x \sin (x y)) \vec{j}$