Answer
$1$
Work Step by Step
$A$ = $\int_{{\,0}}^{{\,2\ln2}}$ $(e^{\frac{x}{2}}-e^{\frac{-x}{2}})$$dx$
$A$ = $(2e^{\frac{x}{2}}+2e^{\frac{-x}{2}})$$|_{{\,0}}^{{\,2\ln2}}$
$A$ = $[(2e^{\ln2}+2e^{-\ln2})-(2e^{0}+2e^{0})]$
$A$ = $[(4+1)-(2+2)]$
$A$ = $1$
