Question

Cálcule a integral abaixo

Answer 1

Cambio de variable

$u=\sin x\to du=\cos x dx\\ \\ x=0\Rightarrow u=0\\ \\ x=\dfrac{\pi}{2}\Rightarrow u=1\\ \\ \displaystyle \int_{0}^{\pi/2}e^{\sin x}\cos x dx=\int _{0}^{1}e^udu\\ \\ \int_{0}^{\pi/2}e^{\sin x}\cos x dx=\left.e^u\right|_0^1\\ \\ \boxed{\int_{0}^{\pi/2}e^{\sin x}\cos x dx=e-1}$