question_answer

If \[\text{ }\!\!\Delta\!\!\text{ }\left( \text{x} \right)\left| \begin{matrix}    \text{1} & \text{cosx} & \text{1-cosx}  \\    \text{1+sinx} & \text{cosx} & \text{1+sinx-cosx}  \\    \text{sinx} & \text{sinx} & \text{1}  \\ \end{matrix} \right|\], then \[\int_{0}^{\pi /4}{\Delta }\left( x \right)dx\] is equal to

A) \[\frac{1}{4}\]                                   

B) \[\frac{1}{2}\]

C)  0                                            

D) \[-\frac{1}{4}\]

Correct Answer: D

Solution :

Given, \[l=\frac{15}{200}=7.5\times {{10}^{-2}}A\] Applying               =