<p>Area of region formed by points <i>(x, y)</i> satisfying <i>[x]</i><sup>2</sup> = <i>[y]</i><sup>2</sup> for <i>0</i> ≤ <i>x</i> ≤ <i>4</i> is equal to (where [ ] denotes greatest integer function)</p>
Step-by-Step Solution
Key Concept: Identify the regions where [x]² = [y]² for each integer value of [x], then calculate the total area by summing contributions from each strip.
<p><strong>Solution:</strong> The condition <i>[x]</i><sup>2</sup> = <i>[y]</i><sup>2</sup> means <i>[x]</i> = ±<i>[y]</i>.</p><p>For 0 ≤ <i>x</i> ≤ 4, we have <i>[x]</i> ∈ {0, 1, 2, 3, 4}.</p><p>The region consists of points where <i>[y]</i> = <i>[x]</i> or <i>[y]</i> = -<i>[x]</i>.</p><p>Computing areas for each strip and summing: Total area = 7.</p><p>∴ Answer is <strong>R (7)</strong>.</p>
Correct Answer: R