Evaluate `int (x)/(5x^2-2) dx`

Answer

D

Explanation

`d(P,OA)le min[d(P,OB),d(P,AB)]`
or `d(P,OA)le(P,OB)`
and `d(P,OA0)le d(P,AB)`
When `d(P,OA)P` is equidistant from OA and OB, or P lies on the bisector of lines OA and OB.
Hence, when `d(P,OA)le d(P,OB)`, point P is nearer to OA than to OB or lies below the angle bisector of `angleAOB`. Similarly, when `d(P,OA)led(P,AB)P` is nearer to OA than to AB, or P lies below the bisector of `angle OAB and AB`. Therefore, the required area is equal to the area of `DeltaOIA`. Now,
`tanangleBOA=(sqrt3)/(1)=sqrt3`
or `angle BOA=60^@`
Hence, the triangle is equilateral. then I coincides. with the centroid which is `(1,1//sqrt3)`.
Therefore,the area of `Delta OIA` is
`(1)/(2) OAxxIM=(1)/(2)xx2xx(1)/(sqrt3)=(1)/(sqrt3)`sq.units