Question

Area of the region satisfying $x \leq 2, y \leq|x|, x-$ axis and $x \geq 0$ is:

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

Answer 1

Answer: (C)

2 sq unit

Answer 2

Required area $=$ Area of shaded region $OAB$
$={ }_{0}^{2} ydx ={ }_{0}^{2} xdx =\frac{ x ^{2}}{2}_{0}^2$
$=2$ sq unit
Alternate Solution
Required area $=$ Area of $\triangle OAB$
$=\frac{1}{2} \times 2 \times 2$
$=2 \,sq$ unit