Question

f(x) = $\left| \begin{matrix} 2\cos^{2}2x & \sin 2x & - \sin x \\ \sin 2x & 2\sin^{2}x & \cos x \\ \sin x & - \cos x & 0 \end{matrix} \right|$The value of $\int_{0}^{\pi/2}{f´(x)}$

dx is equal to

• A. –2
• B. –1
• C. 2
• D. 0

Answer 1

Answer: (D)

0

Answer 2

$\int_{0}^{\pi/2}{f´(x)dx}$ = f$\left( \frac{\pi}{2} \right)$ – f(0) = $\left| \begin{matrix} 2 & 0 & - 1 \\ 0 & 2 & 0 \\ 1 & 0 & 0 \end{matrix} \right|$ – $\left| \begin{matrix} 2 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & - 1 & 0 \end{matrix} \right|$

= 2 – 2 = 0