Home > Area Under the Curve > Premium Question > AUC-Q12

Area Under the Curve

Area Between Two Curves

Premium Question

Grade 12

Question:

The area bounded by the curves $y = x^2$ and $y = \sqrt{x}$ is:

(1) $\frac{1}{3}$

(2) $\frac{1}{6}$

(3) $\frac{1}{12}$

(4) $\frac{2}{3}$

Step-by-Step Solution

Key Concept: Find the intersection points of $y = x^2$ and $y = \sqrt{x}$, then integrate $(\sqrt{x} - x^2)$ between these limits.

The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.

Correct Answer: (1)