Numerical integration numerical integration attempts to estimate the value of a definite integral without solving for the indefinite integral; i. e. , estimate the value of without solving for recall the first fundamental theorem of calculus 2
Numerical integration 3
Aside many symbolic math programs can solve for the indefinite integral if the integral can be expressed in terms of elementary functions how do they do this? 4 http: //en. wikipedia. org/wiki/Risch_algorithm
Numerical integration 5
Rectangle (or midpoint) rule 6
Rectangle (or midpoint) rule 7
Trapezoid rule 8
Trapezoid rule 9
Simpson's rule 10
Simpson's rule 11
Composite rules 12
Composite rectangle (or midpoint) rule 13
Composite rectangle (or midpoint) rule 14
Composite trapezoid rule 15
Composite trapezoid rule 16
Composite Simpson's rule 17
In class exercise implement composite rectangle, trapezoid, and Simpson's rule test implementations using known integrals 18
Numerical integration in MATLAB provides functions for integration using the trapezoidal rule a more sophisticated composite rule (global adaptive quadrature) 19 trapz integral, integral 2, integral 3