Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Determinants
Answer
Comment
Share
Q)

If $f(x)=\begin{vmatrix}\cos x&1&0\\1&2\cos x&1\\0&1&2\cos x\end{vmatrix}$ then $\int\limits_0^{\large\frac{\pi}{2}}2f(x)dx$ is equal to

$\begin{array}{1 1}(A)\;\large\frac{2}{3}&(B)\;\large\frac{-2}{3}\\(C)\;1&(D)\;-1\end{array}$

1 Answer

Comment
A)
Given :
$f(x)=\begin{vmatrix}\cos x&1&0\\1&2\cos x&1\\0&1&2\cos x\end{vmatrix}$
On expansion we get
$f(x)=\cos x(4\cos^2x-1)-2\cos x$
$\Rightarrow 4\cos^3x-3\cos x=\cos 3x$
$\int\limits_0^{\large\frac{\pi}{2}}2f(x)dx=2\int\limits_0^{\large\frac{\pi}{2}}\cos 3xdx$
$\Rightarrow 2\big[\large\frac{\sin 3x}{3}\big]_0^{\large\frac{\pi}{2}}$
$\Rightarrow -\large\frac{2}{3}$
Hence (B) is the correct answer.
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
...