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The area of the region R={(x,y):|x| le|y...

The area of the region `R={(x,y):|x| le|y| and x^2+y^2le1}` is

A

` (1)/(2)ltalphalt1`

B

`alpha^(4)+4alpha^(2)-1=0`

C

`0ltalphale(1)/(2)`

D

`2alpha^(4)-4alpha^(2)+1=0`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Area between `y=x^(3) and y= x" in "x in (0,1)` is
`A=overset(1)underset(0)int(x-x^(3))dx=(1)/(4)`
Area of curvilinear triangle `OPQ=(A)/(2)=(1)/(8)`
`rArr" "overset(alpha)underset(0)int(x-x^(3))dx=(1)/(8)`
`rArr" "2alpha^(4)-4alpha^(2)+1=0`
`rArr" "(alpha^(2)-1)^(2)=(1)/(2)`
`rArr" "alpha^(2)=(sqrt(2)-1)/(sqrt(2))`
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