Using antiderivative to find velocity from acceleration

[Ether]

Some useful vocabulary and definitions:

- an antiderivative of a function f(x) is any function whose derivative equals f(x)

- "indefinite integral" and "antiderivative" are, in most contexts, synonyms

- the definite integral of f(x) evaluated over the range x=a to x=b can be calculated analytically if an antiderivative for f(x) can be found. If F(x) is an antiderivative of f(x), then the afore-mentioned definite integral is equal to F(b)-F(a). Loosely speaking, this amazing fact is known as the Fundamental Theorem of Calculus.

- not all functions f(x) have an antiderivative expressable with elementary functions

- definite integrals can be approximated using numerical methods. A very simple method, often called Euler's method, is to simply sum up the values of f(x) at equal intervals in the range and multiply the sum by the interval. Other more accurate methods are available, such as Runge-Kutta. These methods are often available in numerical computation libraries.

- in the real world, integrating a sensor signal to obtain a new signal is fraught with difficulties. jitter and rounding errors can create signals which are not accurate. proceed with caution.