Trapezium Rule (Numerical Integration) (Edexcel A-Level Mathematics): Flashcards

It gives an overestimate of the area under the curve.

The upper bound is $25$ when $x$ is at its maximum value.

Area = $\int_0^5 x^2 dx = \frac{125}{3} \approx 41.67$.

It uses rectangles that touch the curve's left-hand side.

Use the smallest value of $x$, then square it.

LB is min, UB is max value of the integrand over the interval.

It provides an estimate of the area under a curve.

The tops of trapeziums lie above the curve.

Using $h = 1$, result: $\frac{85}{2}$.

Using more or thinner strips enhances accuracy.