Overview
Integration is the reverse of differentiation — it finds the original function from its gradient.
The rule
∫ xⁿ dx = xⁿ⁺¹ ÷ (n + 1) + c (for n ≠ −1)
Always add the constant of integration, + c, for an indefinite integral.
Standard integrals
- ∫ (ax + b)ⁿ dx = (ax + b)ⁿ⁺¹ ÷ [a(n + 1)] + c
- ∫ eˣ dx = eˣ + c
- ∫ cos x dx = sin x + c, ∫ sin x dx = −cos x + c
Finding c
If you know a point on the curve, substitute it after integrating to find c.
Worked example
∫ (6x² + 2) dx = 2x³ + 2x + c. If the curve passes through (0, 5), then c = 5.
Common mistakes
- Forgetting the + c on an indefinite integral.
Exam tips
- Check your answer by differentiating it — you should get back the original.