The area (in sq. units) of the region described by (x, y) / y^2 2 x . and .y (4 x-1) is

Step-by-step solution

Putting x= y^2 2 in y=4 x-1 , we get aligned & y=4 ( y^2 2 )-1 2 y^2-y-1=0 & (y-1)(2 y+1)=0 & y=1, -1 2 aligned Required area aligned & = _ -1 / 2 ^1 ( y+1 4 ) d y- _ -1 / 2 ^1 y^2 2 ~d y & = 1 4 [ y^2 2 +y ]_ -1 / 2 ^1- 1 2 [ y^3 3 ]_ -1 / 2 ^1 & = 1 4 [ ( 1 2 - 1 8 )+ (1+ 1 2 ) ]- 1 2 ( 1 3 + 1 24 ) & = 1 4 ( 15 8 )- 1 2 ( 9 24 ) & = 15 32 - 3 16 & = 9 32 aligned