f ( x ) = | * 20 c 2 ^2 2x & 2x & - x 2x & 2 ^2 x & x x & - x &0 … - Vidyadip

MCQ

$f\left( x \right) = \left| {\begin{array}{*{20}{c}}
{2{{\cos }^2}2x}&{\sin 2x}&{ - \sin x} \\
{\sin 2x}&{2{{\sin }^2}x}&{\cos x} \\
{\sin x}&{ - \cos x}&0
\end{array}} \right|$,the value of $\int\limits_0^{\frac{\pi }{2}} {f'\left( x \right)} \,dx$ is equal to

A
$-2$
B
$-1$
C
$2$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
$\int_{0}^{\pi / 2} f(x) d x=[f(x)]_{0}^{\frac{\pi}{2}}=f\left(\frac{\pi}{2}\right)-f(0)$

$f(\pi / 2)-f(0)=\left|\begin{array}{ccc}{2} & {0} & {-1} \\ {0} & {2} & {0} \\ {1} & {0} & {0}\end{array}\right|-\left|\begin{array}{ccc}{2} & {0} & {0} \\ {0} & {0} & {1} \\ {0} & {-1} & {0}\end{array}\right|=0$

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