1.

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

Answer»

`(4pi - sqrt3)/(6)`
`(4pi - sqrt3)/(4)`
`(4pi + sqrt3)/(6)`
NONE of these

Solution :
`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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