MATLAB has multiple integration routines:
https://www.mathworks.com/help/matlab/ref/integral.html#References
References:
[1] L.F. Shampine “Vectorized Adaptive Quadrature in MATLAB®,” Journal of Computational and Applied Mathematics, 211, 2008, pp.131–140.
https://www.mathworks.com/help/matlab/ref/quad.html
Algorithms
quad implements a low order method using an adaptive recursive Simpson's rule. References
[1] Gander, W. and W. Gautschi, “Adaptive Quadrature – Revisited,” BIT, Vol. 40, 2000, pp. 84-101. This document is also available at http://www.inf.ethz.ch/personal/gander.
https://www.mathworks.com/help/matlab/ref/quadgk.html#f94-1004038
Algorithms
quadgk implements adaptive quadrature based on a Gauss-Kronrod pair (15th and 7th order formulas). References
[1] L.F. Shampine “Vectorized Adaptive Quadrature in MATLAB®,” Journal of Computational and Applied Mathematics, 211, 2008, pp.131–140.
https://www.mathworks.com/help/matlab/ref/quadl.html#f94-998971
Algorithms
quadl implements a high order method using an adaptive Gauss/Lobatto quadrature rule. References
[1] Gander, W. and W. Gautschi, “Adaptive Quadrature – Revisited,” BIT, Vol. 40, 2000, pp. 84-101. This document is also available at http://www.inf.ethz.ch/personal/gander.
