Question

The intercept made by the tangent to the curve $y={\int }_0^x|t|dt,$ which is parallel to the line $y=2x,$ on $x$ -axis is equal to

• A. $1$
• B. $-2$
• C. $2$
• D. None of these

Answer 1

The correct option is A $1$

$\begin{array}{c}y={\int }_0^x\left|t\right|dt\\ \frac{dy}{dx}=\left|x\right|\\ 2=\left|x\right|\\ x=\pm 2\\ then,y={\int }_0^x\left|t\right|dt\\ when,x=2then,\\ y={\int }_0^2\left|t\right|dt\\ =2\\ wherex=-2\\ y={\int }_0^{-2}\left|t\right|dt\\ =-2\\ equationof\tan gents-\\ \left(y-2\right)=2\left(x-2\right)\\ y-2=2x-4\\ y=2x-2--------\left(1\right)\\ y-2=-2\left(x+2\right)\\ y-2=-2x-4\\ y=-2x-2-------\left(2\right)\\ from\left(1\right)and\left(2\right)\\ x=\pm 1\end{array}$

Hence,

option $\left(A\right)$ is correct answer.