Question

Area bounded by the curve $x=0$ and $x+2\left|y\right|=1$ is

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $1$
• D. $2$

Answer 1

The correct option is B

$\frac{1}{2}$

Explanation for the correct option:

Step 1. Draw the graphs of $x=0$ and $x+2\left|y\right|=1$:

Given that $x=0$

and $x+2\left|y\right|=1$

$\Rightarrow$ $y=\frac{1-x}{2}$

Step 2. Area of bounded region $=$Area of $ACOA$

$=2$ area of $OABO$

$$\begin{gathered} =2{\int }_0^1\left(\frac{1-x}{2}\right)dx \\ ={\left[x-\frac{x^2}{2}\right]}_0^1 \\ =\frac{\mathbf{1}}{\mathbf{2}} \end{gathered}$$

Hence, Option ‘B’ is Correct.