substitution notation

The following are two commonly used substitution notations for calculating definite integrals with the antiderivative:

  • β€’


  • β€’


Here, the right hand the difference  F⁒(b)-F⁒(a).  For example, one has


In Finland (only?) the corresponding notation is


which may be somewhat better;  it is read in same manner as the definite integral notation, β€œsijoitus 1:stΓ€ 2:een ln x” (literally: β€œsubstitution from 1 to 2  ln x”).  The position of the substitution symbol in front of the function to be substituted is perhaps more natural in the sense that the symbol has an operator (as e.g. the summing symbol).  One of benefits of the Finnish notation is that one can comfortably clarify in it which is the variable to be substituted (as in the sum notation), e.g. in the case


The notation


is extended also to such cases as



  • β€’


  • β€’


  • β€’


  • β€’


Note.  There are in Finland also some other β€œnational”, unofficial mathematical notations used in universities, e.g.


which means β€˜such that’.  For example, one may write

Title substitution notation
Canonical name SubstitutionNotation
Date of creation 2013-03-22 15:08:12
Last modified on 2013-03-22 15:08:12
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 18
Author pahio (2872)
Entry type Topic
Classification msc 26A42
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