Let $\mathbf { F } ( x , y , z ) = x \mathbf { j }$

question 180

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = x \mathbf { j }$ . Evaluate the line integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ along the elliptical path $\mathbf { r } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j } + \cos t \mathbf { k } , 0 \leq \mathrm { t } \leq 2 \pi$ .

• A) \(\pi\)
• B) \(\pi \sqrt { 2 }\)
• C)\(\pi \sqrt { 3 }\)
• D)\(2 \pi\)
• E) \(\frac { \sqrt { 2 } } { 2 } \pi\)
• F) \(\frac { \sqrt { 3 } } { 2 } \pi\)
• G) \(\frac { \pi } { 2 }\)
• H) \(\frac { \pi } { 4 }\)

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Definitions:

Mushroom

A type of fungus characterized by a cap and stem, with many species producing edible or medicinal fruiting bodies.

Herbivore

Primary consumer in a grazing food chain; a plant eater.

Plant Foods

Edible parts of plants, including fruits, vegetables, grains, nuts, and seeds, that are consumed by humans and other herbivores.

Detritus-Feeders

Organisms that feed on dead organic material, contributing to decomposition and nutrient cycling.