Evaluate the Line Integral Along the Curve C $\int _ { C } \left( 18 x ^ { 2 } + 5 e ^ { 5 y } + \frac { 1 } { z + 1 } \right) d s , C$

question 198

Multiple Choice

Evaluate the line integral along the curve C.
- $\int _ { C } \left( 18 x ^ { 2 } + 5 e ^ { 5 y } + \frac { 1 } { z + 1 } \right) d s , C$ is the path from $( 0,0,0 )$ to $( 1,1,1 )$ given by:
$C _ { 1 } : r ( t ) = t i , 0 \leq t \leq 1$
$C _ { 2 } : r ( t ) = i + t j , 0 \leq t \leq 1$
$C _ { 3 } : r ( t ) = i + j + t k , 0 \leq t \leq 1$

• A) \(43 + 5 e ^ { 5 } + \ln 2\)
• B) \(17 + e ^ { 5 }\)
• C) \(23 + \mathrm { e } ^ { 5 }\)
• D) \(48 + 6 e ^ { 5 } + \ln 2\)

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