# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution

## Class StandardInterval

• java.lang.Object
• com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution.StandardInterval
• All Implemented Interfaces:
SubstitutionRule

public class StandardInterval
extends Object
implements SubstitutionRule
This transformation is for mapping integral region from [a, b] to [-1, 1]. The substitution rule is $\int_{a}^{b}f(x)dx = \int_{-1}^{1}\frac{b-a}{2}f(\frac{(b-a)t+(a+b)}{2})dt$
• ### Constructor Summary

Constructors
Constructor and Description
StandardInterval(double a, double b)
Construct a StandardInterval substitution rule.
• ### Method Summary

All Methods
Modifier and Type Method and Description
UnivariateRealFunction dx()
the first order derivative of the transformation: x'(t) = dx(t)/dt
double ta()
Get the lower limit of the integral.
double tb()
Get the upper limit of the integral.
UnivariateRealFunction x()
the transformation: x(t)
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### StandardInterval

public StandardInterval(double a,
double b)
Construct a StandardInterval substitution rule.
Parameters:
a - the lower limit
b - the upper limit
• ### Method Detail

• #### x

public UnivariateRealFunction x()
Description copied from interface: SubstitutionRule
the transformation: x(t)
Specified by:
x in interface SubstitutionRule
Returns:
x(t)
• #### dx

public UnivariateRealFunction dx()
Description copied from interface: SubstitutionRule
the first order derivative of the transformation: x'(t) = dx(t)/dt
Specified by:
dx in interface SubstitutionRule
Returns:
x'(t) = dx(t)/dt
• #### ta

public double ta()
Description copied from interface: SubstitutionRule
Get the lower limit of the integral.
Specified by:
ta in interface SubstitutionRule
Returns:
the lower limit
• #### tb

public double tb()
Description copied from interface: SubstitutionRule
Get the upper limit of the integral.
Specified by:
tb in interface SubstitutionRule
Returns:
the upper limit