Trapezoidal Rule (Leaving Cert Mathematics): Flashcards

It approximates the area under a curve or integral.

Width $h$, function values $f(x_0)$, $f(x_1)$, ..., $f(x_n)$.

$h = (b - a) / n$, where $[a, b]$ is the interval.

Divide the interval $[a, b]$ into $n$ equal parts.

Evaluate $f(x)$ at each division point $x_0,...,x_n$.

Area $\approx \frac{h}{2} [f(x_0) + 2f(x_1) + ... + f(x_n)]$

The area was found using numerical approximation methods.

Two intervals were used in Example 2.

The trapezoidal rule is used in Example 2.

It approximates continuous functions over an interval.