Integration
Lesson 4 of 11
Definite integrals and area
Objective. Evaluate definite integrals and interpret them as area.
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
Practice
Each question comes with a picture and a listen button. Try it first, then reveal the answer.
Your progress
Tick each step as you finish it — Continue brings you back here.
0 of 4 steps complete