Integration · Year 12
In Year 12 you learn: integrating powers of x.
Integration reverses differentiation. If you know a gradient function, integrating gives back the original function plus a constant. Definite integrals add up infinitely many thin strips. So they give areas under curves, distances from velocities and totals from rates.
Key facts
- ∫ ax^n dx = (ax^(n+1))/(n + 1) + c for n ≠ −1. Also ∫ 1/x dx = ln|x| + c.
- An indefinite integral needs + c. A known point on the curve fixes c.
- Integrating a rate gives a total: distance = ∫ v dt and water collected = ∫ (flow rate) dt.