Area Under the Curve
Area with log bounds
Grade 12
Question:
<p>Area of the region \(\{(x,y)\,:\,y\ge0,\,y\le x,\,y\le 2-x\}\). [JEE Main 2023]</p>
<li>\(1\)</li>
<li>\(\dfrac{1}{2}\)</li>
<li>\(2\)</li>
<li>\(\dfrac{3}{4}\)</li>
Step-by-Step Solution
Key Concept: Region bounded by y=0, y=x (line from origin), y=2-x (line). Triangle with vertices (0,0),(1,1),(2,0). Area=(1/2) \cdot 2 \cdot 1=1.
<div class='solution'>
<p>Vertices: $y=x$ and $y=2-x$ meet at $(1,1)$. Both meet y=0 at $(0,0)$ and $(2,0)$. Triangle with base 2, height 1. Area $=\frac{1}{2}\cdot2\cdot1=\boxed{1}$. ✓</p>
</div>
Correct Answer: A