Find the area bounded by the curve `y=sqrtx,x=2y+3` in the first quadrant and X-axis.

Answer

N/a

Explanation

Given equation of the curves are `y=sqrtx" and " x=2y+3` in the first quadrat.
On solving both the equations for y, we get
`y=sqrt(2y+3)`
`rArr y^(2)=2y+3`
`rArr y^(2)-2y--3=0`
`rArr y^(2)-3y+y-3=0`
`rArr y(y-3)+1(y-3)=0`
`rArr (y-1)(y-3)=0`
`rArr y=-1, 3`
`:. " Required area of shaded region,"`
`A=int_(0)^(3)(2y+3-y^(2))dy=[(2y^(2))/2+3y-(y^(3))/3]_(0)^(3)`
`=[18/2+9-9-0]=9 " sq units"`