Set $up,$ but $do$ not evaluate, $an$ integral for the length $of$ the curve.

$y=e^{x}sinx,0x\frac{}{2}$

Select the correct answer.

$L={\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}\sqrt[\phantom{2}]{1-e^{2x}(1-sin2x)}dx$

$L={\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}\sqrt[\phantom{2}]{1+e^{2x}(1-sin2x)}dx$

$L={\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}\sqrt[\phantom{2}]{1-e^{2x}(1+sin2x)}dx$

$L={\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}\sqrt[\phantom{2}]{1+e^{2x}(1+sin2x)}dx$