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
- 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
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Common questions
What is the 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. It is one of the applications of integrals formulas in the CalcRef reference.
What do the symbols in the Area Between Curves mean?
In the Area Between Curves, a is the left bound; b is the right bound.
How do you use the Area Between Curves?
Worked example. 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.
Practice
Quiz yourself on Applications of Integrals
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