Find the area of the region bounded by the curves y = x² + 2, y = x, x = 0 and x = 3.

We are to find the area of the region bounded by the curves
y = x² + 2,
y = x,
x = 0
and x = 3
Now y = x² + 2 is an upward parabola with vertex (0, 2).
y = x is a straight line passing through the origin,
(3, 3) and lies below the parabola.

Now area bounded by the parabola, above the x-axis and ordinates x = 0, x = 3

Area bounded by the line y = x, above the x-axis and ordinates x = 0, x = 3