Find the area of the region included between y² = 9x and y = x

In y² = 9x parabola it is not defined for negative values of x hence the parabola will be to the right of Y-axis passing through (0, 0)

And y = x is a straight line passing through origin

We have to find area between y² = 9x and y = x shown below

To find intersection point of parabola and line solve parabola equation and line equation simultaneously

Put y = x in y² = 9x

⇒ x² = 9x

⇒ x = 9

Put x = 9 in y = x we get y = 9

Hence point of intersection is (9, 9)

⇒ area between parabola and line = area under parabola – area under line …(i)

Let us find area under parabola

⇒ y² = 9x

⇒ y = 3√x

Integrate from 0 to 9

Now let us find area under straight line y = x

y = x

Integrate from 0 to 9

Using (i)

⇒ area between parabola and line = 54 – 40.5 = 13.5 unit²

Hence area bounded is 13.5 unit²