Find the area of the region bounded by `y=sqrt(x)a n dy=xdot`

Explanation

The given equations are ,
`y=sqrt(x).....(1)`and
`y=x........(2)`
from`(1)` and `(2)` we get,
`y(y – 1) = 0 `
So, `y = 0` or `y = 1` and `x = 0` or `x = 1`
On solving these two equations, we get the points of intersection.
The points are `O (0, 0)` and `A(1,1)`.
Hence, Bounded Area, `A = (text[Area between the curve (i) and x axis from 0 to 1]) -( text[Area between the curve (ii) and x axis from 0 to 1] )`
so, Area
`A=int_0^1(sqrtx-x)dx`
`=[2/3xsqrt(x)-x^2/2]_0^1`
`=[2/3(1)sqrt1-1^2/2]`
`=1/6` sq units.