The function y=f(x) is the solution of t...

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)`

Verified by Experts

The correct Answer is:

B

Similar Questions

Explore conceptually related problems

sqrt(3)x^(2) - sqrt(2)x + 3sqrt(3)=0

The value of sin^(-1)(-sqrt(3)/2)\ is: (A) (-pi)/3 (B) (-2pi)/3 (C) (4pi)/3 (D) (5pi)/3

Find angle between the lines y - sqrt3x - 5 0 " and " sqrt3 y - x +6 = 0 .

int_(-1)^( sqrt3) (dx)/( 1+x^2) = …...... .

The value of x in (0,pi/2) satisfying (sqrt(3)-1)/(sinx)+(sqrt(3)+1)/(cosx)=4sqrt(2) is/are (a) pi/(12) (b) (5pi)/(12) (c) (7pi)/(24) (d) (11pi)/(36)

Find the value of cos [cos^(-1) ((-sqrt3)/2) + pi/6]

Evaluate the following (i) sin ( pi/2 - sin^(-1) ( (-1)/2)) (ii) sin(pi/2 - sin^(-1)(- sqrt3/2))

The range of the function f(x)=sqrt(x-1)+2sqrt(3-x) is

The value of x which satisfy the equation (sqrt(5x^2-8x+3))-sqrt((5x^2-9x+4))=sqrt((2x^2-2x))-sqrt((2x^2-3x+1)) is