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MathidiaMathematics Academy
Integration techniques
Lesson 9 of 11
Introduction

Definite integrals and area

Objective. Evaluate a definite integral and interpret it as an area.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Integrate, then substitute the upper limit and subtract the value at the lower limit. Regions below the axis give negative contributions.

Worked example

Evaluate ∫₀² 3x² dx.

3
Illustrated card showing 3
  1. 1Integral of 3x² is x³.
  2. 2Upper: 2³ = 8. Lower: 0³ = 0.
  3. 38 − 0 = 8.

Answer: 8

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Practice

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Common mistake. Adding the constant of integration to a definite integral.

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