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

Interface SubstitutionRule

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

DoubleExponential, DoubleExponential4HalfRealLine, DoubleExponential4RealLine, Exponential, InvertingVariable, MixedRule, NoChangeOfVariable, PowerLawSingularity, StandardInterval

public interface SubstitutionRule
extends java.io.Serializable

A substitution rule specifies \(x(t)\) and \(\frac{\mathrm{d} x}{\mathrm{d} t}\).

We set /[ x = x(t) t = x^{-1}(x) = t(x) /] such that, /[ \int_{a}^{b} f(x)\,dx = \int_{t(a)}^{t(b)} f(x)x'(t)\, dt /]

See Also:

Wikipedia: Integration by substitution

Method Summary

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)

Method Detail

x

UnivariateRealFunction x()

the transformation: x(t)

Returns:

x(t)

dx

UnivariateRealFunction dx()

the first order derivative of the transformation: x'(t) = dx(t)/dt

Returns:

x'(t) = dx(t)/dt

ta

double ta()

Get the lower limit of the integral.

Returns:

the lower limit

tb

double tb()

Get the upper limit of the integral.

Returns:

the upper limit