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  • The intercepts on x-axis made by tangents to the curve , <img alt="y= \int_{0}^{x}\left | t \right |dt,x\epsilon R" src="https://learn.careers360.com/latex-image/?%5Cdpi%7B100%7D%20y%3D%20%5Cint_%7

The intercepts on x-axis made by tangents to the curve , y= \int_{0}^{x}\left | t \right |dt,x\epsilon R,which are parallel to the line y = 2x ,are equal to:

Option: 1

\pm 4


Option: 2

\pm 1


Option: 3

\pm 2


Option: 4

\pm 3


Answers (1)

best_answer

As we have learned

NEWTON LEIBNITZ THEOREM -

\frac {d}{dt}\left ( \int_{f(t)}^{\phi (t))}F(x)dx \right )=F(\phi(t))\phi^{'}(t)-F(f(t))f^{'}(t)

-

 

 \frac{dy}{dx } = |x |  

We have , dy/dx = 2 

So,  x = \pm 2

For x = 2 

y = \int_{0}^{2} |t|dt = 1/2 \times 2\times 2 = 2

 

So , (y-2) = 2 (x-2)

 \Rightarrow 2x-y -2 = 0

x- intercept = 1 

Similarly for x = -2 

x intercept = -1 

 

 

 

 

 

Posted by

Suraj Bhandari

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