Question

Let f : [0, π] → $\R$ be the function defined by
$f(x)=\begin{cases} (x-\pi)e^{\sin x} & \text{if } 0 \le x \le \frac{\pi}{2},\\\ xe^{\sin x}+\frac{4}{\pi} & \text{if }\frac{\pi}{2}\lt x \le \pi. \end{cases}$
Then the value of
$\int\limits_0^{\pi}f(x)dx$
is equal to _________. (Rounded off to two decimal places)

Answer 1

The correct answer is : 2.