Question

The intercepts on $x$-axis made by tangents to the curve, $y={\int }_0^x|t|$ dt, $x\in R$, which are parallel to the line $y=2x$, are equal to

• A. $\pm 2$
• B. $\pm 3$
• C. $\pm 4$
• D. $\pm 1$

Answer 1

The correct option is D $\pm 1$

$\frac{dy}{dx}=|x|=2\Rightarrow x=\pm 2\Rightarrow y={\int }_0^2|t|$ dt $=2$ for $x=2$
and $y={\int }_0^{-2}|t|$ dt $=-2$ for $x=-2$
Hence the equations of the tangents are
$y-2=2(x-2)\Rightarrow y=2x-2$
and $y+2=2(x+2)\Rightarrow y=2x+2$
Putting $y=0$, we get $x=1$ and $-1$.