Integration as the limit of a sum (AQA A-Level Mathematics): Flashcards

Limit of sum of areas of rectangles under a curve

Area under curve $y=f(x)$ over interval $[a,b]$

Delta x = rac{b-a}{n}

$S_n = sum_{i=1}^n f(x_i^*) Delta x$

Better approximation of area under curve

$int_a^b f(x)dx = lim_{n o infty} sum_{i=1}^n f(x_i^*) Delta x$

Left endpoint of each subinterval

Right endpoint of each subinterval

Midpoint of each subinterval

Trapezoids rather than rectangles