Allied & ICAR Exam Bank • ALLIED_0037 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

The area enclosed between the parabola $y = x^2$ and the line $y = x$ from $x = 0$ to $x = 1$ is:

Answer Key:

0.167

Step-by-Step Solution & Explanation

Area $= \int_0^1 (x - x^2) dx = \left[ \frac{x^2}{2} - \frac{x^3}{3} \right]_0^1 = \frac{1}{2} - \frac{1}{3} = \frac{1}{6} \approx 0.167$.
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