Question $15(4$ points$)$

Evaluate the line integral of $f(x,y)$ along the curve C$.$

$f(x,y)=4y^2,C$:$y=e^{-x},0x2$

$2[2\sqrt[\phantom{2}]{2}-(e^{-4}+1{)}^{\frac{3}{2}}]$

$\frac{4}{3}[(2{)}^{\frac{3}{2}}-2\sqrt[\phantom{2}]{2}]$

$\frac{4}{3}[2\sqrt[\phantom{2}]{2}-(e^{-4}+1{)}^{\frac{3}{2}}]$

$\frac{4}{3}[2\sqrt[\phantom{2}]{2}-(2{)}^{\frac{3}{2}}]$