Area Under the Curve
Area between parabola and line
Grade 12

Question:

<p>The area (in sq. units) bounded between the parabola \(y=x^2\) and the line \(y=x\) is: [MAU007]</p>
1/6
1/3
1/2
1/12

Step-by-Step Solution

Key Concept: Intersection: x^2=x \to x=0,1. Area = \int_0^1(x-x^2)dx.
<div class='solution'> <p>Intersections: $x=x^2\Rightarrow x=0,1$. On $[0,1]$: $x\ge x^2$.</p> <p>$$A=\int_0^1(x-x^2)\,dx=\left[\frac{x^2}{2}-\frac{x^3}{3}\right]_0^1=\frac{1}{2}-\frac{1}{3}=\boxed{\frac{1}{6}}$$</p> </div>
Correct Answer: A

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