Answer
$1$
Work Step by Step
Our aim is to integrate the integral as follows:
$ Area =\iint_D dA $
$\int^{ln2}_{0} \int^{e^x}_{0} \space dy \space dx =\int^{ln (2)}_{0} [e^x]\space dx $
or, $=[e^x]^{\ln2}_0$
or, $=e^{\ln 2}-e^{0}$
or, $=1$