(Solved): Consider the vector field \( \bar{F}= \) Is this vector field Conservative? If so: Find a function ...

Consider the vector field \( \bar{F}=<2 x+7 y, 3 x+2 y> \) Is this vector field Conservative? If so: Find a function \( f \) so that \( \bar{F}=\nabla f \) \[ f(x, y)=\quad+K \] Use your answer to evaluate \( \int_{C} \bar{F} \cdot d \bar{r} \) along the curve \( \mathrm{C}: \bar{r}(t)=t^{2} \bar{i}+t^{3} \bar{j}, \quad 0 \leq t \leq 2 \)