Question

Qual o valor da expressão:
$\int\limits^ \frac{ \pi }{2} _0 {(sen x + cos x)} \, dx$

Answer 1

$\int (\sin{x}+\cos{x}).\mathrm{dx}=\int \sin{x}.\mathrm{dx}+\int \cos{x}.\mathrm{dx}=\\ = -\cos{x}+\sin{x}\ \to\ f(x)=\sin{x}-cos{x}\\\\ \int\limits_0^\frac{\pi}{2}(\sin{x}+\cos{x}).\mathrm{dx}=f(\frac{\pi}{2})-f(0)=\\\\ =(\sin{\frac{\pi}{2}}-\cos{\frac{\pi}{2})-(\sin{0}-\cos{0})}=\\\\ =(1-0)-(0-1)=1+1=\mathbf{2}$