The work done by the force $\mathbf { F } ( x , y ) = - x ^ { 2 } y \mathbf { i } + 2 y \mathbf { j }$ moving along $\mathbf { r } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j }$ with $0 \leq t \leq \frac { \pi } { 2 }$ is

A) $\frac { 16 - \pi } { 8 }$
B) $\frac { \pi + 16 } { 8 }$
C) $\frac { \pi + 16 } { 16 }$
D) $\frac { 16 - \pi } { 16 }$
E) $\frac { \pi + 16 } { 32 }$

Question

The work done by the force

\mathbf { F } ( x , y ) = - x ^ { 2 } y \mathbf { i } + 2 y \mathbf { j }

moving along

\mathbf { r } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j }

with

0 \leq t \leq \frac { \pi } { 2 }

is

A) $\frac { 16 - \pi } { 8 }$
B) $\frac { \pi + 16 } { 8 }$
C) $\frac { \pi + 16 } { 16 }$
D) $\frac { 16 - \pi } { 16 }$
E) $\frac { \pi + 16 } { 32 }$

Quizplus · Accepted Answer

The Answer of The work done by the force $\mathbf { F } ( x , y ) = - x ^ { 2 } y \mathbf { i } + 2 y \mathbf { j }$ moving along $\mathbf { r } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j }$ with $0 \leq t \leq \frac { \pi } { 2 }$ is

A) $\frac { 16 - \pi } { 8 }$
B) $\frac { \pi + 16 } { 8 }$
C) $\frac { \pi + 16 } { 16 }$
D) $\frac { 16 - \pi } { 16 }$
E) $\frac { \pi + 16 } { 32 }$

The Work Done by the Force F(x,y)=−x2yi+2yj\mathbf { F } ( x , y ) = - x ^ { 2 } y \mathbf { i } + 2 y \mathbf { j }F(x,y)=−x2yi+2yj

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