integral over a period interval
Theorem. If the real function is periodic and integrable (http://planetmath.org/RiemannIntegrable) over a period (http://planetmath.org/Periodic) interval, the value of integral over a period interval is always the same, i.e.
(1) |
where is the period of .
Proof. The right hand side of the equation (1) is manipulated, with one substitution (http://planetmath.org/ChangeOfVariableInDefiniteIntegral) :
References
- 1 Ernst Lindelöf: Johdatus korkeampaan analyysiin. Fourth edition. Werner Söderström Osakeyhtiö, Porvoo ja Helsinki (1956).
- 2 Fråga Lund om matematik, http://www.maths.lth.se/query/here.