Ordinary integral:
Generally speaking, it is to find the original function of the integrand, and then bring the upper and lower bounds into the evaluation (definite integral)
The obtained solution is an exact solution.
See College Course: Advanced Mathematics.
In matlab, the function: int () can be used to solve.
Numerical integration:
Because most integrals in practical engineering can't find the original function.
Therefore, it is difficult to get an exact solution.
In order to be able to calculate the results, some Daniel (Newton, Gauss, etc. ) The numerical solution is worked out.
Namely: numerical integration (the error of the exact solution meets the needs)
There are many specific methods, such as:
Trapezoidal formula; Simpson formula; Recursive formula; Lattice integral; Adaptive integration; Gauss-Legendre integral and so on.
See Postgraduate Course: Numerical Analysis.
There are some numerical integral functions in matlab:
Trapz (): Based on complex trapezoidal formula
Integral (): Solving the unary numerical integral
Integral2 (): Solving the Numerical Solution of Double Integral in General Region
Integral3 (): Solving the Numerical Solution of Triple Integral in General Region
Personally, I often use Gauss quadrature method to get numerical integration.
Generally speaking, a numerical solution with sufficient accuracy can be obtained by taking 10-20 Gaussian points.
Finally: Please call me Lei Feng!