MCQ
The value of ${\int\limits_0^x {\left| {\cos \,x} \right|} ^3}\,dx$ is
- ✓$0$
- B$\frac{4}{3}$
- C$\frac{2}{3}$
- D$-\frac{4}{3}$
$ \Rightarrow 2\int\limits_0^{\frac{\pi }{2}} {{{\left| {\cos x} \right|}^3}} dx$
$ \Rightarrow 2\int\limits_0^{\frac{\pi }{2}} {{{\left( {\cos x} \right)}^3}} dx$
$\Rightarrow 2\left(\frac{2}{3}\right)=\frac{4}{3} \text { (By wallis formula) }$
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$\left|\begin{array}{ccc}\cos ^{2} x & 1+\sin ^{2} x & \sin 2 x \\ 1+\cos ^{2} x & \sin ^{2} x & \sin 2 x \\ \cos ^{2} x & \sin ^{2} x & 1+\sin 2 x\end{array}\right|$.
Then the ordered pair $( m , M )$ is equal to