Find the Value of the Line Integral $\mathbf { r } ( t ) = 3 \cos t \mathbf { i } + 3 \sin t \mathbf { j } + 8 \mathbf { k } , 0 \leq t \leq \pi$

Multiple Choice

Find the value of the line integral $\int_{c} \mathbf { F } \text {. } d \mathbf { r } \text {, where } \mathbf { F } ( x , y ) = e ^ { y } ( z \mathbf { i } + x z \mathbf { j } + x \mathbf { k } ) \text { and }$ $\mathbf { r } ( t ) = 3 \cos t \mathbf { i } + 3 \sin t \mathbf { j } + 8 \mathbf { k } , 0 \leq t \leq \pi$
(Hint: If $\mathbf { F }$ is conservative, the integration may be easier on an alternate path.)

A) - 24
B) 48
C) - 48
D) 24
E) 0