The area of the shaded region
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
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
Area A= ∫abfy-gydy
So, the area of the shaded region is
A= ∫01[y-(y2-1 ]dy
By taking the upper and the lower limit of integration,
Therefore, the area of shaded region is 43.