Consider the Two-Dimensional Vector Field $\vec { F } ( x , y ) = - 4 y \vec { i } + 2 x \vec { j }$

question 1

Essay

Consider the two-dimensional vector field $\vec { F } ( x , y ) = - 4 y \vec { i } + 2 x \vec { j }$ Write down parameterizations of the three line segments C₁, C₂, and C₃ shown in the figure below. Use your parameterizations to compute the line integral $\int _ { C _ { 3 } + C _ { 2 } - C _ { 1 } } \vec { F } \cdot d \vec { r }$ by finding $\int_{G_{1}} \vec{F} \cdot d \vec{r}, \int_{C_{2}} \vec{F} \cdot d \vec{r}$ and $\int _ { C _ { 3 } } \vec { F } \cdot d \vec { r }$

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Definitions:

Income Effect

The variation in a person's or economy's earnings and the effect of this variation on the demanded quantity of a product or service.

Ernst Ludwig Kirchner

A German expressionist painter and printmaker, one of the founders of the Die Brücke group, known for his vibrant colors and stark representations of modern life.

Expressive Use

The utilization of artistic elements in a way that evokes emotions or expresses an artist's emotional experience.

Formal Elements

Fundamental visual components of art such as line, shape, color, texture, and space, which are combined to create artworks.