Question: The function \(\varphi(x, y)=x \cos \left(y^{2}\right)\) is a potential for \(\vec{F}(x, y)=\left\langle\cos \left(y^{2}\right),-2 x y \sin \left(y^{2}\right)\right\rangle\).

Use that fact to compute \(\int_{C} \vec{F} \cdot d \vec{s}\) where \(C\) is the path made up of straight line segments from \(P=(2,0)\) to \(Q=(5,-3 \pi)\) to \(R=(3, \sqrt{\pi})\).

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