1.8.1—Basic integration
- Syllabus
- 9709–2028–2029
- Objective
- 1.8.1
- Level
- AS
Basic integration reverses differentiation and includes a constant
Integrate powers term by term using ∫xⁿdx=xⁿ⁺¹/(n+1)+C for n≠−1. Integration is the family of antiderivatives whose derivative is the original function.
Rewrite expressions into powers first, then integrate each term. Include C for an indefinite integral and differentiate the result to check.
∫(3x²−4x+5)dx=x³−2x²+5x+C.
The constant is not optional in an indefinite integral: different C values represent different antiderivatives.
ConceptA-Level CAIE Mathematics AS