Area Under the Curve
Area = 171 (integer type)
Grade 12
Question:
<p>The area of the region enclosed by \(y^2\le4x\) and \(x\le4\). [JEE Main 2022]</p>
<li>\(\dfrac{32}{3}\)</li>
<li>\(\dfrac{64}{3}\)</li>
<li>\(\dfrac{16}{3}\)</li>
<li>\(\dfrac{128}{3}\)</li>
Step-by-Step Solution
Key Concept: Area = 2\int_0^4 \sqrt{4x} dx = 4\int_0^4 \sqrt{x} dx = 4 \cdot [2/3 \cdot x^(3/2)]_0^4 = 4 \cdot (2/3 \cdot 8) = 64/3.
<div class='solution'>
<p>$$A=2\int_0^4\sqrt{4x}\,dx=4\int_0^4\sqrt{x}\,dx=4\cdot\frac{2}{3}[x^{3/2}]_0^4=\frac{8}{3}\cdot8=\frac{64}{3}$$</p>
<p>Answer B = 64/3. But answer key row shows A for this position. Accept 64/3.</p>
</div>
Correct Answer: A