Integration

Integration Methods

With this tutorial we analyse various implementations of numerical integration mechanisms. This tutorial only works on one-dimensional files but the dimensional dependence is only present in some distinct points.

Tasks

L1: Assign a function $f(x) = x^2$ on all vertices. This function is used as integrand.

L1: Approximate the integral by using the

Hints
- Trapezoidal rule: $\int_a^b f(x) dx = \frac{f(a)+f(b)}{2} \cdot (b-a)$
- A second testfile is located in the lesson folder. Create a few different testfiles in order to see the effect
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rectangular rule: $\int_a^b f(x) dx \approx f(a) \cdot (b-a)$

middle point rule: $\int_a^b f(x) dx \approx \frac{b-a}{2} \cdot (b-a)$

trapezoid rule: $\int_a^b f(x) dx \approx \frac{f(a) + f(b)}{2} \cdot (b-a)$

simpson rule: $\int_a^b f(x) dx \approx \frac{b-a}{6}\left[f(a) + 4f\left(\frac{a+b}{2}\right)+f(b)\right]$

Integration Methods

Tasks

Hints

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