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The intercepts on x-axis made by tangent...

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 (1) `+-2` (2) `+-3` (3) `+-4` (4) `+-1`

A

`+-1`

B

`+-2`

C

`+-3`

D

`+-4`

Text Solution

Verified by Experts

The correct Answer is:
A
`y=int_(0)^(x)|t|dt`
Case I: If `xgt0`
`y=int_(0)^(x)tdt=[(t^(2))/2]_(0)^(x)=(x^(2))/2implies(dy)/(dx)=x=2` (given)
`implies x=2` and `y=2`
`:.` eqution of tangent is `(y-2)=2(x-2)`
or `y-2x+2=0`
Hence `x` intercept `=`
Case II: `xlt0`
`-y=int_(0)^(pi)-tdt=[(-t^(2))/2]_(0)^(x)=(-x^(2))/2`
`:.(dy)/(dt)=-x=2`
`:. x=-2,:.y=-2`,
`:.` equation iof tangent is `y+2=2(x+2)`
or `2x-y+2=0`
`:.x` intencept `=-1`
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