Area Under the Curve
Area — horizontal strips
Grade 12
Question:
<p>The area bounded by \(y^2=4x\) and \(x=1\) is: [MAU017]</p>
<li>\(\dfrac{8}{3}\)</li>
<li>\(\dfrac{4}{3}\)</li>
<li>\(\dfrac{2}{3}\)</li>
<li>\(\dfrac{16}{3}\)</li>
Step-by-Step Solution
Key Concept: Area = 2\int_0^\sqrt[1]{4x}dx = 2 \cdot 2\int_0^1\sqrt{x} dx = 4 \cdot [2/3] = 8/3.
<div class='solution'>
<p>Area = \(2\int_0^1\sqrt{4x}\,dx = 4\int_0^1\sqrt{x}\,dx = 4\cdot\left[\frac{2}{3}x^{3/2}\right]_0^1 = \frac{8}{3}\)</p>
</div>
Correct Answer: A