1.

The intercepts on x-axis made by tangents to thecurve, `y=int_0^x|t|dt , x in R ,`which are parallel to the line `y""=""2x`, are equalto(1) `+-2`(2) `+-3`(3) `+-4`(4) `+-1`

Answer» `y = int_0^x |t| dt`
`dy/dx = |x|= 2`
`x +- 2`
when `x=2`
`y = int_0^2 |t|dt`
`= |t|^2/2 = 2`
when `x=-2`
`y= - int_0^-2 |t| dt`
`= - [|t|^2/2]`
`y= -2`
now,`y-2 = 2(x-2)`
`y-2 = 2x - 4`
`y= 2x -2`
`y-2 = -2(x+2)`
`y-2 = -2x - 4`
`y = -2x-2`
so, by solving `2x-2= 0`
`x=1`
`0= -2x-2`
`x=-1`
`x= +- 1`
Answer is option 4


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