Question

Calcule a integral da função f(x)=|sen(x)|, em [−π,π].

Answer 1

$\int\limits^{\pi}_{-\pi} {f} \, dx \|\ \ f(x)=\sin(x)+|\sin(x)|\| \\ \int\limits^{\pi}_{-\pi} {\sin(x)} \, dx +\int\limits^{\pi}_{-\pi} {\sin(x)} \, dx =-cos(x)|\limits^{\pi}_{-\pi}+cos(x)|^{\pi}_{-\pi}\\ -(\cos(\pi)-\cos(-\pi))+\cos(\pi)-\cos(\pi)=-(-1-1)+(-1+1)=\\ -(-2)+0=2$
$\int\limits^{\pi}_{-\pi} {\sin(x)} \, dx +\int\limits^{\pi}_{-\pi} {\sin(x)} \, dx=2$