Practice question · Multiple choice
Numerical integration approximates an integral by summing values at sample points. Why does a computer use these methods routinely, when the Fundamental Theorem offers an exact route?
Hints
- To use the Fundamental Theorem you need an antiderivative. How often do you have one?
- Ask what happens when the integrand is a table of sensor readings.
Show the answer
D. Because most functions have no antiderivative in elementary form.
Why
The Fundamental Theorem is exact and conditional: it needs an antiderivative, and most integrands have none in elementary form, e^(−x²) being both the standard case and central to statistics. The commoner situation is that there is no formula at all, only sensor readings or simulation output. So quadrature is the general method and the theorem the lucky special case.
Practise The Definite Integral and Area
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