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)\(0\)

---

Definitions:

Andrew Carnegie

A 19th-century industrialist and philanthropist who led the expansion of the American steel industry.

Baby Boom

The significant increase in the birth rate, particularly noted in the period following World War II.

Suburbanization

The process by which urban areas expand outward, primarily due to increased housing development and commercial activities in suburb areas.

West German Industrial Production

Refers to the output of industrial goods and services in the Western part of Germany, particularly relevant before the reunification of East and West Germany in 1990.