Find a function $f$ such that $\mathbf { F } = \nabla f$, and use it to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ along the given curve $C$.
$$\begin{array} { l }
\mathbf { F } ( x , y ) = x ^ { 3 } y ^ { 4 } \mathbf { i } + y ^ { 3 } x ^ { 4 } \mathbf { j } \
C : \mathbf { r } ( t ) = \sqrt { t } \mathbf { i } + \left( 1 + t ^ { 3 } \right) \mathbf { j } , 0 \leq t \leq 1
\end{array}$$

Question

Find a function $f$ such that $\mathbf { F } = \nabla f$, and use it to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ along the given curve $C$.
$$\begin{array} { l } 
\mathbf { F } ( x , y ) = x ^ { 3 } y ^ { 4 } \mathbf { i } + y ^ { 3 } x ^ { 4 } \mathbf { j } \
C : \mathbf { r } ( t ) = \sqrt { t } \mathbf { i } + \left( 1 + t ^ { 3 } \right) \mathbf { j } , 0 \leq t \leq 1
\end{array}$$

Quizplus · Accepted Answer

The Answer of Find a function $f$ such that $\mathbf { F } = \nabla f$, and use it to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ along the given curve $C$.
$$\begin{array} { l } 
\mathbf { F } ( x , y ) = x ^ { 3 } y ^ { 4 } \mathbf { i } + y ^ { 3 } x ^ { 4 } \mathbf { j } \
C : \mathbf { r } ( t ) = \sqrt { t } \mathbf { i } + \left( 1 + t ^ { 3 } \right) \mathbf { j } , 0 \leq t \leq 1
\end{array}$$

Find a Function fff Such That F=∇f\mathbf { F } = \nabla fF=∇f

Find a Function $f$ Such That $\mathbf { F } = \nabla f$