Find the area of region bounded by the line x = 2 and the parabola y² = 8x

In y² = 8x 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 x = 2 is a straight line parallel to Y-axis

Plot the equation y² = 8x and x = 2 and the area as shown

So we have to integrate y² = 8x that is y = 2√2√x from 0 to 2

But observe that integrating the parabola equation from 0 to 2 will give the area OBC that is area under the parabola in 1^st quadrant

We have to find the whole shaded region ODBC

Parabola y² = 8x is symmetric about X-axis hence the area above X-axis that is in 1^st quadrant is equal to area below X-axis that is in 4^th quadrant hence areaOBC = areaOBD

Hence area bounded by parabola and line will be twice the area which we will get by integration parabola from 0 to 2

areaODBC = 2 × areaOBC …(i)

let us find area under parabola

⇒ y² = 8x

⇒ y = 2√2√x

Integrate from 0 to 2

Using (i)

The shaded areaOCBD = 2 ×

Hence area bounded = unit²