Estimating the Area Under a Graph (VCE SSCE Mathematical Methods): Flashcards

Left-endpoint, Right-endpoint, Trapezium rule

Trapezium rule

Overestimate (larger than true area)

Underestimate (smaller than true area)

$\frac{1}{2}(a + b)h$ ($a,b$ parallel sides, $h$ height)

Average of left-endpoint and right-endpoint estimates

First & last once, intermediate values multiplied by 2

$\int_a^b f(x) \, dx$

Integrand

More accurate estimate