Examples for

Numerical Integration

Many different numerical integration methods exist for approximating the value of an integral. Wolfram|Alpha provides tools for solving otherwise intractable integrals numerically. Specify an integration algorithm, such as Simpson's method, and compare it against alternative methods.

Numerical Integration

Use numerical integration to solve integrals that lack a closed form solution.

Numerically integrate functions that cannot be integrated symbolically:

integrate sin(cos x) from x=0 to 1
integrate sqrt( (1+x^2)/(1+x^4) ) dx, x=0..1

Numerical Integration Methods

Compute integrals using specified numerical integration algorithms.

Approximate an integral using a specified numerical method:

integrate x cos x from 1 to 3 with left endpoint method
right endpoint rule x^3-x^2 on [1,2] with 10 intervals
integrate using midpoint method x e^x
5 interval trapezoidal rule integrate sinx cosx on [0,4]
Simpson's rule 2+1/(sqrt(x))+1/(4*x) on [2,5] with interval size 0.5
integral (x^2-2)/x dx from 1 to 2 using Boole's rule

Compare the performance of different methods:

left end point method vs. simpson's rule for x cos x from 1 to 3

RELATED EXAMPLES

  • Area between Curves
  • Integrals
  • Numerical Analysis
  • Numerical Differential Equation Solving
  • Numerical Root Finding