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The area bounded by the curves y=|x|-1a ...

The area bounded by the curves `y=|x|-1a n dy=-|x|+1` is 1 sq. units (b) 2 sq. units `2sqrt(2)` sq. units (d) 4 sq. units

A

`alpha=e^(2)+1`

B

`alpha=e^(2)-2`

C

`beta=1+e^(-1)`

D

`beta=1+e^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
`"Solving given curves "y=(1)/(x^(2)),y=(1)/(4(x-1))," we get "`
`x^(2)=4(x-1)rArr(x-2)^(2)=0`
So, curves touch other at x=2.

`therefore" "A=overset(a)underset(2)int((1)/(4(x-1))-(1)/(x^(2)))dx=(1)/(a)`
`rArr" [(1)/(4)log(x-1)+(1)/(x)]_(2)^(a)=(1)/(a)`
`rArr" "(1)/(4)log(a-1)+(1)/(a)-(1)/(2)=(1)/(a)`
`rArr" " log(a-1)=2`
`rArr" "a=e^(2)+1`
`"Also "1-(1)/(b)=overset(2)underset(0)int((1)/(4(x-1))-(1)/(x^(2)))dx`
`rArr" " b=1+e^(-2)`
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