Area Under the Curve
Area between curves — multiple correct
Grade 12
Question:
<p>For \(f(x)=x^2\) and \(g(x)=2x\), which are correct? [MAU041]</p>
Intersection at x=0 and x=1
Intersection at x=0 and x=2
Area between curves = 4/3
Area between curves = 1/3
Step-by-Step Solution
Key Concept: x^2=2x \to x=0,2. Area=\int_0^2(2x-x^2)dx = [x^2-x^3/3]_0^2 = 4-8/3 = 4/3.
<div class='solution'>
<p>$x^2=2x\Rightarrow x(x-2)=0\Rightarrow x=0,2$. ✓ (B)</p>
<p>$A=\int_0^2(2x-x^2)dx=[x^2-\frac{x^3}{3}]_0^2=4-\frac{8}{3}=\frac{4}{3}$. ✓ (C)</p>
</div>
Correct Answer: ['B', 'C']