#### To determine

**To find:**

The area of the shaded region

#### Answer

9

#### Explanation

**1) Concept:**

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

A= ∫abfy-gydy

**2) Given:**

3) **Calculation:**

From the given graph,

we have that x=2y-y2 is the right boundary curve and x=y2-4y is the left boundary curve.

Let, fy=2y-y2 and gy=y2-4y

The shaded region lies between y=0 to y=3

Formula-

Area A= ∫abfy-gydy

So, the area of the shaded region is

A= ∫03[2y-y2-(y2-4y]dy

=∫036y-2y2dy

=6y22-2y33 03

=3y2-2y3303

By taking the upper and the lower limits of integration.

=332-2333

=3·9-2·273

=27-18

=9

Therefore, the area of the shaded region is 9

**Conclusion:**

The area of the shaded region is 9