Evaluate the Line Integral of F(x,y) Along the Curve C $$f ( x , y ) = 2 y ^ { 2 } , C : y = e ^ { - x } , 0 \leq x \leq 4$$

Multiple Choice

Evaluate the line integral of f(x,y) along the curve C.
- $$f ( x , y ) = 2 y ^ { 2 } , C : y = e ^ { - x } , 0 \leq x \leq 4$$

A) $1 \left[ 2 \sqrt { 2 } - \left( e ^ { - 8 } + 1 \right) ^ { 3 / 2 } \right]$
B) $\frac { 2 } { 3 } \left[ ( 4 ) ^ { 3 / 2 } - 2 \sqrt { 2 } \right]$
C) $\frac { 2 } { 3 } \left[ 2 \sqrt { 2 } - ( 4 ) ^ { 3 / 2 } \right]$
D) $\frac { 2 } { 3 } \left[ 2 \sqrt { 2 } - \left( e ^ { - 8 } + 1 \right) ^ { 3 / 2 } \right]$