Let `f(x)=|{:(2cos^(2)x,,sin2x,,-sinx),(sin2x,,2sin^(2)x,,cosx),(sinx,,-cosx,,0):}|`. Then the value of `int_(0)^(x//2) [f(x)+f'(x)]dx` is

Options

A. `pi`
B. `pi//2`
C. `2pi`
D. None of these

Answer

A

Explanation

`C_(1) rarr C_(f) - 2 sinx C_(3)`
`C_(2) rarr C_(2) + 2 cosx C_(3)`
`f(x) = |{:(2,,0,,-sinx),(0,,2,,cosx),(sinx,,-cosx,,0):}|`
`f'(x) = 0`
`rArr overset(pi//2)underset(0)(int)(f(x)+f'(x))dx = overset(pi//2)underset(0)int2dx = 2 xx (pi)/(2) = pi`