Definite Integration

Current version of ArtSGraph does not have a function to perform indefinite integration (i.e. finding of function’s antiderivative).

However ArtSGraph has a function for approximate calculation of Definite Integral of a function of one variable. ArtSGraph uses Simpson’s method, which proves to be very accurate in many cases. 

 

To calculate definite integral, use function  

 

I(F,x,a,b)

 

where

F stands for integrand,

x is the variable of integration,

a and b specify lower and upper limits of integration respectively. 

 

Example

I(sin(x),x,0,pi)                          ; Result: 2

 

By default ArtSGraph uses Simpson method with 100 steps.  You can specify number of steps explicitly using 5th argument,  i.e.

 

I(F,x,a,b,n)

 

where n specifies number of steps. Compare

 

f=x^3

I(f,x,0,1,4)

I(f,x,0,1,10)

I(f,x,0,1,100)

I(f,x,0,1,1000)