∑ Mathematics LabNumerical Integration · v1.7.1 Beta

MATHEMATICS LAB

Numerical Integration

Approximate a definite integral and see how numerical methods estimate its value and reduce the error.

Implicit multiplication is supported (3x, 2(x+1)); use ^ for powers. Functions: sin, cos, tan, exp, ln, log, sqrt, abs, asin, acos, atan, sinh, cosh, tanh. Constants: pi, e.

Simpson’s 1/3 rule: n must be even. Simpson’s 3/8 rule: n must be divisible by 3.

Examples: x^2 in [0,2] · exp(-x^2) in [0,1] · sin(x) in [0,π]

Geometric representation

The orange curve represents f(x). The blue regions show the selected method’s geometric approximation; for Simpson’s rules, these are interpolating polynomials, not the original curve.