Home
Class 12
MATHS
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`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|38 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Numerical)|28 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

The intercepts made by the tangent to the curve y=int_(0)^(x) |t| dt, which is parallel to the line y=2x on y-axis are equal to

A tangent to the curve y= int_(0)^(x)|x|dt, which is parallel to the line y=x, cuts off an intercept from the y-axis is equal to

Find the equation of the tangent to the curve x^2+3y-3=0 , which is parallel to the line y=4x-5 .

Find the equation of tangent of the curve y^(2) = 4x+5 which is parallel to the line 2x-y=5 .

Find the equation of tangent to the curve 2x^(2)-y=7 , which is parallel to the line 4x-y+3=0 .

find the equation of tangent to the curve y=sqrt(3x-2) which is parallel to the the line 4x-2y+5=0

Find the equation of the tangent to the curve y=sqrt(5x-3) , which is parallel to the line 4x-2y+3=0 .