Integration

Numerical Integration Methods

With this tutorial we analyse various implementations of numerical integration mechanisms.

L1: Create a data structure, e.g., an array, which stores simple x coordinates and another double value.

L1: Assign the value of the function $f(x) = x^2$ to all array elements. This function is used as integrand.

L2: Approximate the integral by using the

Hints
- Trapezoidal rule: $\int_a^b f(x) dx = \frac{f(a)+f(b)}{2} \cdot (b-a)$
More Information

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