Find the work done by the force field $\mathbf { F } ( x , y ) = 2 x y \mathbf { i } + x ^ { 2 } \mathbf { j }$ on a particle that moves along the curve $\mathbf { r } ( t ) = t ^ { 2 } \mathbf { i } + t ^ { 3 } \mathbf { j } , \quad 1 \leq t \leq 2$ .
A) $127$
B)$128$
C) $63$
D) $64$
E) $31$
F)$32$
G) $15$
H)$16$

Question

Find the work done by the force field $\mathbf { F } ( x , y ) = 2 x y \mathbf { i } + x ^ { 2 } \mathbf { j }$ on a particle that moves along the curve $\mathbf { r } ( t ) = t ^ { 2 } \mathbf { i } + t ^ { 3 } \mathbf { j } , \quad 1 \leq t \leq 2$ .
A) $127$
B)$128$ 
C) $63$ 
D) $64$ 
E) $31$ 
F)$32$
G) $15$ 
H)$16$

Quizplus · Accepted Answer

The work done by the force field is calculated by evaluating the line integral $\int_C \mathbf{F} \cdot d\mathbf{r}$. Substituting $\mathbf{r}(t)$ into $\mathbf{F}$ and computing the integral from $t=1$ to $t=2$, the result is $127$.

Find the Work Done by the Force Field F(x,y)=2xyi+x2j\mathbf { F } ( x , y ) = 2 x y \mathbf { i } + x ^ { 2 } \mathbf { j }F(x,y)=2xyi+x2j

Find the Work Done by the Force Field $\mathbf { F } ( x , y ) = 2 x y \mathbf { i } + x ^ { 2 } \mathbf { j }$