Introduction to Integration
Integration is the reverse process of differentiation and is used to find areas under curves and accumulate quantities.
What You Need to Know
Key Concept Diagram
The indefinite integral reverses differentiation, adding a constant of integration C
The definite integral calculates the exact area under a curve between two bounds
Basic power rule for integration: ∫xⁿ dx = xⁿ⁺¹/(n+1) + C for n ≠ −1
The Fundamental Theorem of Calculus links differentiation and integration
Key Vocabulary
Integral
The result of the integration operation, representing accumulated area or quantity
Antiderivative
A function whose derivative equals the original function being integrated
Constant of Integration
The arbitrary constant C added to every indefinite integral
Definite Integral
An integral evaluated between specific lower and upper bounds, giving a numerical result
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is ∫x³ dx?
Question 2
What does the constant of integration C represent?
Question 3
Evaluate ∫₀² 2x dx.
Key Concepts Summary
- ●The indefinite integral reverses differentiation, adding a constant of integration C
- ●The definite integral calculates the exact area under a curve between two bounds
- ●Basic power rule for integration: ∫xⁿ dx = xⁿ⁺¹/(n+1) + C for n ≠ −1
- ●The Fundamental Theorem of Calculus links differentiation and integration