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The function y=f(x) is the solution of the differential equation `[dy]/[dx]+[xy]/[x^2-1]=[x^4+2x]/sqrt[1-x^2]` in (-1, 1), satisfying `f(0)=0`. Then `int_[-sqrt3/2]^[sqrt3/2] f(x)dx` is (A) ` pi/3 - sqrt3/2` (B) ` pi/3 - sqrt3/4` (C) ` pi/6 - sqrt3/4` (D) ` pi/6 - sqrt3/2`

A

`(pi)/(3)-(sqrt3)/(2)`

B

`(pi)/(3)-(sqrt3)/(4)`

C

`(pi)/(6)-(sqrt3)/(4)`

D

`(pi)/(6)-(sqrt3)/(2)`

Text Solution

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The correct Answer is:
B
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