Interface SubstitutionRule
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- All Known Implementing Classes:
DoubleExponential,DoubleExponential4HalfRealLine,DoubleExponential4RealLine,Exponential,InvertingVariable,MixedRule,NoChangeOfVariable,PowerLawSingularity,StandardInterval
public interface SubstitutionRuleA 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
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Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method Description UnivariateRealFunctiondx()the first order derivative of the transformation: x'(t) = dx(t)/dtdoubleta()Get the lower limit of the integral.doubletb()Get the upper limit of the integral.UnivariateRealFunctionx()the transformation: x(t)
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Method Detail
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x
UnivariateRealFunction x()
the transformation: x(t)- Returns:
- x(t)
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dx
UnivariateRealFunction dx()
the first order derivative of the transformation: x'(t) = dx(t)/dt- Returns:
- x'(t) = dx(t)/dt
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ta
double ta()
Get the lower limit of the integral.- Returns:
- the lower limit
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tb
double tb()
Get the upper limit of the integral.- Returns:
- the upper limit
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