Evaluate the Line Integral Along the Curve C $\int _ { C } ( y + z ) d s , C$

question 3

Multiple Choice

Evaluate the line integral along the curve C.
- $\int _ { C } ( y + z ) d s , C$ is the path from $( 0,0,0 )$ to $( 6 , - 6,1 )$ given by:
$C _ { 1 } : r ( t ) = 6 t ^ { 2 } i - 6 t j , 0 \leq t \leq 1$
$C _ { 2 } : \mathbf { r } ( \mathrm { t } ) = 6 \mathbf { i } - 6 \mathbf { j } + ( t - 1 ) \mathbf { k } , 1 \leq \mathrm { t } \leq 2$

• A) \(- 15 \sqrt { 5 } + \frac { 5 } { 2 }\)
• B) \(- \frac { 59 } { 12 }\)
• C) \(- \frac { 83 } { 2 }\)
• D) \(- 15 \sqrt { 5 } - \frac { 5 } { 2 }\)

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