Applications of Integrals · Area
Area Between Curves
The area between two curves f(x) and g(x) from x = a to x = b. Take the absolute value or integrate top minus bottom.
- 2 variables
- 2 worked examples
- 14 in Applications of Integrals
Variables
| Symbol | Name | Unit |
|---|---|---|
| a | Left bound | - |
| b | Right bound | - |
Worked examples
Find the area between y = x² and y = x on [0, 1].
- On [0,1]: x ≥ x², so top - bottom = x - x²
- ∫₀¹ (x - x²) dx = [x²/2 - x³/3]₀¹ = 1/2 - 1/3 = 1/6
Answer: 1/6
1 more worked examplePremium
Find the area enclosed by y = 4 - x² and y = x + 2.
Step-by-step solution locked.
Unlock the full working. CalcRef Premium opens the step-by-step solution above, and 141 worked solutions across the whole library - the intermediate lines, not just the answer. The formula statement, its conditions, its variables and the first worked example stay free on every page.
See all 14 Applications of Integrals formulas on one printable sheet - the same statements and conditions as these pages, typeset and laid out for paper.
Practice
Quiz yourself on Applications of Integrals
Area Between Curves is one of 14 Applications of Integrals formulas in CalcRef, out of 136 in the library. Today's free round is 10 mixed multiple-choice questions drawn from the same dataset as this page, refreshed every day and replayable as often as you like - no account needed.