Numerical integration functions can approximate the value of an integral whether or not the functional expression is known:
When you know how to evaluate the function, you can use
integral to calculate integrals with specified bounds.
To integrate an array of data where the underlying equation is unknown, you can use
trapz, which performs trapezoidal integration
using the data points to form a series of trapezoids with easily computed areas.
For differentiation, you can differentiate an array of data using
gradient, which uses a finite difference formula to calculate numerical
derivatives. To calculate derivatives of functional expressions, you must use the
This example shows how to parametrize a curve and
compute the arc length using
This example shows how to calculate complex line integrals using the
'Waypoints' option of the
This example shows how to split the integration domain to place a singularity on the boundary.
This example shows how to use the
polyint function to integrate polynomial expressions analytically.
This example shows how to integrate a set of discrete velocity data numerically to approximate the distance traveled.
This example shows how to approximate gradients of a function by finite differences.