Question

Find the area bounded by y = 2; y = √x + 2; and y = 2 - x

Answer 1

Let

$y = 2 \qquad \cdots (i)\\ y = \sqrt{x} + 2 \qquad \cdots (ii)\\ y = 2 - x \qquad \cdots (iii)$

We proceed to check the boundary points of the curve.

From (i) and (ii)

$$2=\sqrt x+2\\ \sqrt x = 2-2\\ \sqrt x =0\\ x=0$$

From (i) and (iii)

$$2=2-x\\ x=2-2\\ x=0$$

From (ii) and (iii)

$$\sqrt x + 2 = 2-x\\ \implies x=0$$

Since the value of x is zero for all the three functions, then, the curves not bounded and therefore, NO SOLUTION

A graph of this is shown below: