Integration
Lesson 4 of 11
Introduction
Definite integrals and area
Objective. Evaluate definite integrals and interpret them as area.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Integrate, then substitute the upper limit and subtract the value at the lower limit. Area below the axis counts as negative.
Worked example
Evaluate ∫₁³ 2x dx.
- 1∫2x dx = x².
- 2At x = 3: 9. At x = 1: 1.
- 39 − 1 = 8.
Answer: 8
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