Let $\vec { F } = ( 4 x + 5 y ) \vec { i } + ( 4 x - 4 y ) \vec { j }$ Let $I _ { 1 } = \int _ { C _ { 1 } } \bar { F } \cdot \overline { d r }$ , where C₁ is the line from (0, 0)to (2, 2).
Let $I_{2}=\int_{c_{2}} \vec{F} \cdot \overrightarrow{d r}$ , where C₂ is parameterized by $\vec { r } ( t ) = t \vec { i } + \frac { 1 } { 2 } t ^ { 2 } \vec { j } , \quad 0 \leq t \leq 2$ Notice that both C₁ and C₂go from (0, 0)to (2, 2), but is $I _ { 1 } = I _ { 2 } ?$ Explain.

Question

Let

\vec { F } = ( 4 x + 5 y ) \vec { i } + ( 4 x - 4 y ) \vec { j }

Let

I _ { 1 } = \int _ { C _ { 1 } } \bar { F } \cdot \overline { d r }

, where C₁ is the line from (0, 0)to (2, 2).
Let

I_{2}=\int_{c_{2}} \vec{F} \cdot \overrightarrow{d r}

, where C₂ is parameterized by

\vec { r } ( t ) = t \vec { i } + \frac { 1 } { 2 } t ^ { 2 } \vec { j } , \quad 0 \leq t \leq 2

Notice that both C₁ and C₂go from (0, 0)to (2, 2), but is

I _ { 1 } = I _ { 2 } ?

Explain.

Quizplus · Accepted Answer

The Answer of Let $\vec { F } = ( 4 x + 5 y ) \vec { i } + ( 4 x - 4 y ) \vec { j }$ Let $I _ { 1 } = \int _ { C _ { 1 } } \bar { F } \cdot \overline { d r }$ , where C₁ is the line from (0, 0)to (2, 2). Let $I_{2}=\int_{c_{2}} \vec{F} \cdot \overrightarrow{d r}$ , where C₂ is parameterized by $\vec { r } ( t ) = t \vec { i } + \frac { 1 } { 2 } t ^ { 2 } \vec { j } , \quad 0 \leq t \leq 2$ Notice that both C₁ and C₂go from (0, 0)to (2, 2), but is $I _ { 1 } = I _ { 2 } ?$ Explain.

Let F⃗=(4x+5y)i⃗+(4x−4y)j⃗\vec { F } = ( 4 x + 5 y ) \vec { i } + ( 4 x - 4 y ) \vec { j }F=(4x+5y)i+(4x−4y)j​

Let $\vec { F } = ( 4 x + 5 y ) \vec { i } + ( 4 x - 4 y ) \vec { j }$