Area Under the Curve
Area of region with circle
Grade 12
Question:
<p>The area of the region \(\{(x,y)\,:\,x^2+y^2\le1\le x+y\}\). [JEE Main 2020]</p>
π/4-1/2
π/2-1
π/4+1/2
π/4
Step-by-Step Solution
Key Concept: Unit circle, region above line x+y=1. Circular segment area = sector (90°) - triangle = \pi/4 - 1/2.
<div class='solution'>
<p>Region: inside unit circle AND above/on line $x+y=1$.</p>
<p>Line intersects circle at $(1,0)$ and $(0,1)$. Central angle = 90°.</p>
<p>Sector area $=\frac{\pi}{4}$. Triangle area $=\frac{1}{2}$.</p>
<p>Segment area $=\frac{\pi}{4}-\frac{1}{2}$. ✓</p>
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Correct Answer: A