Draw the rough sketch of `y^2+1=x ,\ xlt=2.` Find the area enclosed by the curve and the line `x=2.`

Explanation

We have to find the area of shaded region.

Required area
= shaded region `{ABCA}`

`=2` (shaded region ACDA) (as it is symmetrical about the `x`-axis)

(the area can be found by taking a small slice in each region of width `Delta x`, then the area of that sliced part will be `y Delta x` as it is a rectangle and then integrating it to get the area of the whole region)

`=2 int_{1}^{2} y d x` (As `{x}` is between `(1,2)` and the value of `{y}` varies)

``
`=2 int_{1}^{2} sqrt{x-1} d x`

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