WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

Numerical Evaluation of Some Definite Integrals

​
f(x)
log(x)(1+100
2
x
​)
numerical evaluation
numerical minus analytic
x
0.836
This Demonstration shows a trick for computing the definite integral
F(x)=
x
∫
0
f(x)dx
numerically in a given interval of its upper bound
x
using Mathematica. Instead of using NIntegrate we use the function NDSolve. Five test functions are borrowed from reference [1]. Four of these test functions have a singular point at
x=0
. You can plot the analytic solutions of the test integrals as well as the difference of the numerical and analytic solutions as a function of the upper bound variable
x
for different working precisions. The black point on the curve gives the function value
F(x)
when the slider position is at
x
. At the right endpoint these values coincide with the values given in the reference in the details.
Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.