The area bounded by y-axis and the curve x = e^y .sin $\mathrm{\pi }$ y, y = 0, y = 1 is __ sq.units

 Area bounded by y-axis and the curve x = e^y .sin $\mathrm{\pi }$ y, y = 0, y = 1 is 

$\begin{array}{l}A={\int }_0^1 e^y\sin \pi ydy={\left(\frac{e^y}{{\pi }^2+1}(\sin \pi y-\pi \cos \pi y)\right)}_0^1\\ =\frac{(e+1)\pi }{{\pi }^2+1}\end{array}$