Find the work done by F over the curve in the direction of increasing t.
-$$\mathbf { F } = \frac { \mathrm { y } } { \mathrm { z } } \mathbf { i } + \frac { \mathrm { x } } { \mathrm { z } } \mathbf { j } + \frac { \mathrm { x } } { \mathrm { y } } \mathbf { k } ; \mathrm { C } : \mathbf { r } ( \mathrm { t } ) = \mathrm { t } ^ { 7 } \mathbf { i } + \mathrm { t } ^ { 5 } \mathbf { j } + \mathrm { t } ^ { 2 } \mathbf { k } , 0 \leq \mathrm { t } \leq 1$$
A) $W = \frac { 17 } { 10 }$
B) $W = 14$
C) $W = 0$
D) $W = 1$

Question

Quizplus · Accepted Answer

The work done by a force field $\mathbf{F}$ over a curve $\mathbf{r}(t)$ is given by the line integral $\int_C \mathbf{F} \cdot d\mathbf{r}$. Substituting the given expressions and evaluating the integral from $t=0$ to $t=1$ yields $W = \frac{17}{10}$.

Find the Work Done by F Over the Curve in the Direction