The vector field \(F(x,y) = (2x+6y, 6x+7y)\) is: conservative
(If you answered \"not conservative\", enter DNE for the second part.)
A function \(f(x, y)\) that satisfies \(F(x, y) = \nabla f(x, y)\) is:
\(f(x, y) = \)
If C is the curve parameterized by \(\vec{r}(t) = (t^2, t^3)\) for \(0 \le t \le 3\), use the fundamental theorem of line
integrals to compute
\(\int_C \vec{F} \cdot d\vec{r}:\)
