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Area Under the Curve

Area Between Two Curves

IIT-JEE 2005

Grade 12

Question:

The area enclosed between the curve $y = x^2$ and the line $y = x$ is:

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

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

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

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

Step-by-Step Solution

Key Concept: Find the points of intersection of $y = x^2$ and $y = x$ first, then integrate the difference of the upper and lower curves between these limits.

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

Correct Answer: (1)