6) Let $F(x, y) = \begin{bmatrix} \sin(y) - y^2 + 1 \\ x \cos(y) - 2xy \end{bmatrix}$. Is $F$ conservative? If so, give a potential function for $F$. 7) Let $F(x,y) = \begin{bmatrix} \sin(y) - y^2 + 1 \\ x \cos(y) - 2xy \end{bmatrix}$ and let $C$ be the curve $(t^2, 2(\pi - t))$, where $1 \le t \le 2$. Use your work from question 6 to evaluate: $\int_C F \cdot dr$
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To determine if F(x,y) is conservative, we need to check if the partial derivatives of F with respect to x and y are equal. The partial derivative of F with respect to x is: ∂F/∂x = xcosy - 2y The partial derivative of F with respect to y is: ∂F/∂y = -xsin(y) + Show more…
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