$\int_0^{\pi / 2} e^{\sin x} \cdot \cos x d x=$

Question

Aicharya · Accepted Answer

$I=\int_0^{\pi / 2} e^{\sin x} \cos x d x$ Put $\sin x=t$, then at $x=0, t=0$ and at $x=\frac{\pi}{2}, t=1$ and $\cos x d x=d t$ So, $I=\int_0^1 e^t d t=\left[e^t\right]_0^1=e^1-1=e-1$

\(\int_0^{\pi / 2} e^{\sin x} \cdot \cos x d x=\)

Solution