Numerical Methods (AQA A-Level Further Maths): Flashcards

Cannot integrate analytically; experimental data only

Rectangles using y-value at strip centre

$A = \frac{b-a}{n}(y_1 + y_2 + \cdots + y_n)$

$d = \frac{b-a}{n}$ where $[a,b]$ interval, $n$ strips

Uses parabolic curves instead of rectangles

1-4-2-4-2-...-4-2-4-1

Requires even number of strips

$\frac{d}{3}[(y_0+y_n) + 4(\text{odd}) + 2(\text{even})]$

$\frac{\text{approximate} - \text{exact}}{\text{exact}}$

Approximation underestimates exact value