#### To determine

**To find:**

The area of the shaded region.

#### Answer

36

#### Explanation

**1) Concept:**

The area A of a region bounded by the curves y=f(x), y=g(x) and the lines x=a and x=b, where f and g are continuous and f(x)≥ g(x) for all x in a, b is

A= ∫abfx-gxdx

**2) Given:**

3) **Calculation:**

From the given graph,

we can see that y=2x is the top (upper) boundary curve and y=x2-4x is the bottom (lower) boundary curve.

Let, fx=2x and gx=x2-4x

0, 0 and (6, 12) are the pointsof intersection of the given curves.

The shaded region lies between x=0 and x=6

Formula-

Area A= ∫abfx-gxdx

So, the area of the shaded region is

A= ∫062x-(x2-4x) dx

=∫066x-x2dx

=6x22-x33 06

Simplifying,

=3x2-x33 06

By taking the upper and the lower limits of integration,

=362-(6)33-0

=3·36-2163

=108-2163

=108-72

=36

Therefore, the area of the shaded region is 36.

**Conclusion:**

Therefore, the area of the shaded region is 36.