Đáp án:
$\displaystyle\int\limits_0^{\tfrac{\pi}{2}}e^{\sin x}\cos xdx=e-1$
Giải thích các bước giải:
$\quad \displaystyle\int\limits_0^{\tfrac{\pi}{2}}e^{\sin x}\cos xdx$
$= \displaystyle\int\limits_0^{\tfrac{\pi}{2}}e^{\sin x}d(\sin x)$
$=e^{\sin x}\Bigg|_0^{\tfrac{\pi}{2}}$
$= e^{\displaystyle\sin\dfrac{\pi}{2}} - e^{\displaystyle\sin0}$
$= e - 1$