$\mathbf { r } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j } + t ^ { 2 } \mathbf { k } , 0 \leq t \leq \pi$

question 36

Multiple Choice

$\text { Find the value of the line integral } \int _ { C } \mathbf { F } \cdot d \mathbf { r } \text {, where } \mathbf { F } ( x , y ) = 4 \mathbf { i } + 2 z \mathbf { j } + 2 y \mathbf { k } \text { and }$$\mathbf { r } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j } + t ^ { 2 } \mathbf { k } , 0 \leq t \leq \pi$
(Hint: If $\mathbf { F }$ is conservative, the integration may be easier on an alternate path.)

• A) 4
• B) 8
• C) 4.
• D) \(- 4\).
• E) \(- 8\).

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