( ^2 x) , ,dx = ,; ,(x n ,n I) - Vidyadip

MCQ

$\int {\sqrt {({{\sin }^2}x)} } \,\,dx = \,;\,(x \ne n\pi ,n \in I)$

A
$-\cos\, x + c$
B
$\cos \,x + c$
C
$-\cos\, x \,sgn. (\sin \,x) + c$
D
None of these

✓

Answer

$\int|\sin x| d x$
$=\left\{\begin{array}{l}{\int \sin x d x ; \sin x \geq 0} \\ {-\int \sin x d x ; \sin x<0}\end{array}\right.$
$ = \left\{ {\begin{array}{*{20}{c}}
{\int - \cos x;}&{\sin x \ge 0}\\
{\cos x;}&{\sin x < 0}
\end{array}} \right.$
$ = - \cos x{\mathop{\rm \,\,sgn}} \,(\sin x) + c$

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