Numerical integration 1 Numerical integration numerical integration attempts

Numerical integration 1

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