Integration techniques
Lesson 9 of 11
Definite integrals and area
Objective. Evaluate a definite integral and interpret it as an area.
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.
- 1Integral of 3x² is x³.
- 2Upper: 2³ = 8. Lower: 0³ = 0.
- 38 − 0 = 8.
Answer: 8
Practice
Each question comes with a picture and a listen button. Try it first, then reveal the answer.
Common mistake. Adding the constant of integration to a definite integral.
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