Question

Area of the region satisfying $x\le 2,y\le \left|x\right|$ and $x\ge 0$ is

• A. $4$ sq units
• B. $1$ sq units
• C. $2$ sq units
• D. None of these

Answer 1

The correct option is C

$2$ sq units

Explanation for the correct option:

Draw the graph of $x\le 2,y\le \left|x\right|$ and $x\ge 0$:

From the figure, we have

Intersection for the given curves is $\left(2,0\right)$

$\therefore$Required area $=$Area of shaded region $OAB$

$$\begin{gathered} ={\int }_0^{2}ydx \\ ={\int }_0^{2}xdx \\ ={\left[\frac{x^2}{2}\right]}_0^2 \\ =\frac{4}{2} \\ =2 \end{gathered}$$

Thus, Area of the region is $\mathbf{2}$ sq units

Hence, Option ‘C’ is Correct.