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Area of the region satisfying $x \leq 2, y \leq|x|, x-$ axis and $x \geq 0$ is:
Area of the region satisfying $x \leq 2, y \leq|x|, x-$ axis and $x \geq 0$ is:
Updated On: Mar 18, 2024
- 4 sq unit
- 1 sq unit
- 2 sq unit
- None of these
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The Correct Option is C
Solution and Explanation
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
$={ }_{0}^{2} ydx ={ }_{0}^{2} xdx =\frac{ x ^{2}}{2}_{0}^2$
$=2$ sq unit
Alternate Solution
Required area $=$ Area of $\triangle OAB$
$=\frac{1}{2} \times 2 \times 2$
$=2 \,sq$ unit
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