Q115 / 160 · AP EAMCET 2023 (18 May Shift 2) · Mathematics
The area bounded by $y-1=-|x|$ and $y+1=|x|$ is
- A$\frac{1}{2}$
- B1
- Correct answerC2
- D0
Solution
The given curves are
$$
\begin{aligned}
& y-1=-|x| \\
& y+1=|x|
\end{aligned}
$$
Here, $\mathrm{AC}=\sqrt{1+1}=\sqrt{2}$ Area of ACBD $=4$ Area of AOC $=4 \times \frac{1}{2} \times O \mathrm{OAOC}=4 \times \frac{1}{2} \times 1 \times 1=2$ $\therefore$ Area of the required bounded region is 2 .
Here, $\mathrm{AC}=\sqrt{1+1}=\sqrt{2}$ Area of ACBD $=4$ Area of AOC $=4 \times \frac{1}{2} \times O \mathrm{OAOC}=4 \times \frac{1}{2} \times 1 \times 1=2$ $\therefore$ Area of the required bounded region is 2 .
Hence, the correct answer is option: 'C'.