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Area of region enclosed by the region y^...

Area of region enclosed by the region `y^2 le 3x , x^2+y^2 le 4` and `y ge 0` is :

A

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

B

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

C

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

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C

`int _(0) ^(1)sqrt3 sqrtx dx t int _(1)^(2) sqrt(4 -x ^(2)) dx`
`sqrt3 ((x ^(3/2))/(3/2))^(1)+ [(x + sqrt(4-x ^(2)))/(2 ) +4/2 sin ^(-1)""x/2]_(1)^(2)" "[{:(x ^(2) + 3x -4 =0),(x ^(2) + 4x -x -4 =0),(x (x +y)- (x +y) =0),((x-y)(x+y)=0):}`
`(2 sqrt3)/(3) + pi = (sqrt3)/(2) - (pi)/(3)`
`sqrt3((2)/(3) - (1)/(2))+ (2pi)/(3) implies(sqrt3)/(6) + (2pi)/(3) = ( 4pi + sqrt3)/(6)`
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