Draw a rough sketch of the curve in the interval [1, 5]. Find the area under the curve and between the lines x = 1 and x = 5

Squaring both sides

⇒ y² = x – 1

y² = x – 1 is equation of a parabola

In y² = x – 1 parabola it is not defined for values of x less than 1 hence the parabola will be to the right of x = 1 passing through (1, 0)

Now observe that in x ≥ 1 and y has to positive because of square root hence x and y both positive hence the parabola will be drawn only in 1^st quadrant

We have to plot the curve in [1, 5] so just draw the parabolic curve from x = 1 to x = 5 in 1^st quadrant

x = 1 and x = 5 are lines parallel to Y-axis

So we have to integrate from 1 to 5

let us find area under parabolic curve

Integrate from 1 to 5

Hence area bounded = unit²