Find the area of the region lying in the first quadrant bounded by the curve `y^(2)=4x`, X axis and the lines `x=1, x=4`.

Explanation

Area of the shaded region `=underset(1)overset(4)int y.dx`

`=underset(1)overset(4)int 2 sqrt(x).dx (.:'y^(2)=4x "given")`
`=2*(2)/(3)[x^(3//2)]_(1)^(4)`
`=(28)/(3)` sq. units.