Discussion Forum

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

Answer:

Explanation:

Given,  $y=\int_{0}^{x} |t| dt$

  $\therefore$    $\frac{dy}{dx}=|x|.1-0=|x|$

 (by Leibnitz rule)

 $\because$ Tangent to the curve

   $y=\int_{0}^{x} |t| dt,x\in R$   are parallel to the line y=2x

 $\therefore$ slope of both are equal

 $\Rightarrow x=\pm2$

 $\therefore$ points =   $y=\int_{0}^{\pm2} |t|dt=\pm2$

 $\therefore$   Equation of tangent is

   y-2=2(x-2)

and y+2=2(x+2)

 For x- intercept put y=0 , we get

 0-2=2(x-2)

 and 0 +2=2(x+2)= x$\pm$1