Question

If $f(x) = \left| \begin{matrix} x & \cos x & e^{x^{2}} \\ \sin x & x^{2} & \sec x \\ \tan x & 1 & 2 \end{matrix} \right|$ then the value of

$\int_{- \pi/2}^{\pi/2}{f(x)dx}$is equal to

• A. 5
• B. 3
• C. 1
• D. 0

Answer 1

Answer: (D)

0

Answer 2

∴ $f( - x) =$ $\left| \begin{matrix}

• x & \cos x & e^{x^{2}} \
• \sin x & x^{2} & \sec x \
• \tan x & 1 & 2 \end{matrix} \right| = - f(x)$

∴ $\int_{\_\pi/2}^{\pi/2}{f(x)}dx = 0$ $\left\lbrack \because f(x)isoddfunction \right\rbrack$