Definite Integrals

Easymathematics

The value of ∫₀¹ x² dx is

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1/3

1/2

2/3

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About This Question

Subject: mathematics
Chapter: integral calculus
Topic: definite integrals
Difficulty: Easy
Year: 2025

Solution

Correct Answer:

1/3

Find Antiderivative: $\int x^{2} d x = \frac{x ^{3}}{3}$ .
Apply Definite Integral Limits: From $0$ to $1$ .
- $[\frac{x ^{3}}{3}]_{0}^{1}$
Calculation:
- $(\frac{1 ^{3}}{3}) - (\frac{0 ^{3}}{3})$
- $= \frac{1}{3} - 0 = \frac{1}{3}$ .

Geometrically, this is the area under the parabola $y = x^{2}$ between $x = 0$ and $x = 1$ .

This easy difficulty mathematics question is from the chapter integral calculus, covering the topic of definite integrals. It appeared in the 2025 exam.

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Definite Integrals

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Solution

Definite Integrals

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Solution

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Solution

Let $f : R \to R$ be a differentiable function such that $f(x) = x^2 + \int_0^x e^{...

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