MCQ
$\int {\sqrt {({{\sin }^2}x)} } \,\,dx = \,;\,(x \ne n\pi ,n \in I)$
- A$-\cos\, x + c$
- B$\cos \,x + c$
- ✓$-\cos\, x \,sgn. (\sin \,x) + c$
- DNone of these
$=\left\{\begin{array}{l}{\int \sin x d x ; \sin x \geq 0} \\ {-\int \sin x d x ; \sin x<0}\end{array}\right.$
$ = \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$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Which of the following statements is/are $TRUE$ ?
$(A)$ No $a$ satisfies the above equation
$(B)$ An integer $a$ satisfies the above equation
$(C)$ An irrational number $a$ satisfies the above equation
$(D)$ More than one $a$ satisfy the above equation