Evaluate $\int _ { C } \mathbf { F } d \mathbf { r }$

question 78

Multiple Choice

Evaluate $\int _ { C } \mathbf { F } d \mathbf { r }$ where $\mathbf { F } ( x , y ) = \left( e ^ { x ^ { 2 } } + 3 y x ^ { 2 } , \cos y ^ { 2 } + x ^ { 3 } \right)$ and the curve C is given by C : $x = 2 \sin t , y = 2 \cos t , 0 \leq t \leq 2 \pi$ .

• A) \(24 \pi\)
• B)11e
• aa8e2_0f7f_a45e_96ab_39554d580268_TB2033_11
• C)\(48 \pi\)
• D)\(96 \pi\)
• E) \(- 24 \pi\)
• F)\(- 12 \pi\)
• G)\(- 48 \pi\)
• H)\(0\)

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Definitions:

Parasitoid Wasps

Insects that lay their eggs on or in other insects, with the larvae eventually killing the host.

Stabilizing

A type of natural selection that favors the average individuals in a population, thereby maintaining the population's genetic variation.

Directional

In evolutionary biology, a type of natural selection that favors one extreme phenotype over others, causing a shift in the population's phenotypic distribution over time.

Additive Alleles

Alleles that contribute to the phenotype in a way that the effects of individual alleles add up to produce the overall phenotype.