$\int\limits_{0}^{\pi/2} \cos x \, e^{\sin x} \, dx$ is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $e-1$
Let $I = \int\limits_{0}^{\pi/2} \cos x \, e^{\sin x} \, dx$
Put $\sin x = t \Rightarrow \cos x \, dx = dt$
As $x \to 0, \text{then } t \to 0$
and $x \to \pi/2, \text{then } t \to 1$
$∴I = \int\limits_{0}^{1} e^t \, dt = [e^t]_0^1$
$= e^1 - e^0 = e - 1$