Area Under the Curve
Area = 4
Grade 12
Question:
<p>Area of \(\{(x,y)\,:\,x^2\le y\le\sqrt{x}\}\). [JEE Main 2023]</p>
<li>\(\dfrac{1}{3}\)</li>
<li>\(\dfrac{1}{2}\)</li>
<li>\(\dfrac{2}{3}\)</li>
<li>\(1\)</li>
Step-by-Step Solution
Key Concept: \int_0^1(\sqrt{x} - x^2)dx = 2/3 - 1/3 = 1/3.
<div class='solution'><p>$A=\int_0^1(\sqrt{x}-x^2)dx=\frac{2}{3}-\frac{1}{3}=\frac{1}{3}$. ✓</p></div>
Correct Answer: A