#### To determine

**To find:**

The area of the shaded region

#### Answer

43

#### 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 can see that x=y is the right boundary curve and x=y2-1 is theleft boundary curve.

Let, fy=y and gy=y2-1

The shaded region lies between y=0 to y=1

Formula-

Area A= ∫abfy-gydy

So, the area of the shaded region is

A= ∫01[y-(y2-1 ]dy

=∫01[y12-y2+1]dy

=2y323-y33+y 01

By taking the upper and the lower limit of integration,

=23-13+1

=43

Therefore, the area of shaded region is 43.

**Conclusion:**

Therefore, the area of shaded region is 43.