$\large \int_{-\frac {\pi}{4}}^{n\pi - \frac {\pi}{4}} \mid \sin{x} + \cos{x} \mid \ \mathrm{d}x$

For all natural numbers $n$ , find a closed form for the above integral.

$2\sqrt{2}/n$
$2/n$
$2\sqrt{3}/n$
$3n$
$2\sqrt{2}n$
$2\sqrt{5}/n$
$2n$
$3/n$

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too easy !

$\displaystyle{I=\int _{ \cfrac { -\pi }{ 4 } }^{ n\pi -\cfrac { \pi }{ 4 } }{ \left| \sqrt { 2 } \sin { (x+\cfrac { \pi }{ 4 } ) } \right| } dx\\ I=\sqrt { 2 } \int _{ 0 }^{ n\pi }{ \left| \sin { t } \right| } dt=\sqrt { 2 } n\int _{ 0 }^{ \pi }{ \left| \sin { t } \right| dt } \\ I=2\sqrt { 2 } n}$