Find the area of the region included between `y^(2)=9x" and "y=x`.

Answer

N/a

Explanation

We have, `y^(2)=9x`
`rArrx^(2)=9x`
`rArrx^(2)-9x=0`
`rArrx(x-9)=0`
`rArrx=0, 9`

`:. " Area opf shaded region,"A=int_(0)^(9)(sqrt(9x)-x)dx=int_(0)^(9)3x^(1//2)dx-int_(0)^(9)x dx`
`=[3. (x^(3//2))/3 .2]_(0)^(9)-[(x^(2))/2]_(0)^(9)`
`=[(3.3^(2/3xx2))/3 .2-0][81/2-0]`
`=54-81/2=(108-81)/2=27/2" sq units"`