Integration as the limit of a sum (Edexcel A-Level Mathematics): Quizzes

Area under a curve over an interval

$\Delta x = \frac{b - a}{n}$

It becomes a better approximation

$\int_a^b f(x) dx = \lim_{n \to \infty} \sum f(x_i^*) \Delta x$

Left endpoint of each subinterval

Right endpoint of each subinterval

Midpoint of each subinterval

Trapezoids

$\sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}$

$\frac{1}{3}$