Question

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region.

\(y = {\left( {x - 2} \right)^2},y = x\)

Short answer

The area of the region is\(A = \frac{9}{2}\)

Step-by-step solution

Given information

The given value is:

\(y = {\left( {x - 2} \right)^2},y = x\)

The graph

Choose whether to integrate in terms of x or y.

we've got \(y = {(x - 2)^2}\) and \(y = x\)

It will be easy to integrate along the x-axis in this scenario. Let's start by locating the crossings that will serve as integration limits.