Difference between revisions of "Integration by parts for delta integrals with no sigma in integrand"

From timescalewiki
Jump to: navigation, search
 
Line 1: Line 1:
 +
__NOTOC__
 
==Theorem==
 
==Theorem==
 
The following formula holds:
 
The following formula holds:

Latest revision as of 14:48, 13 March 2018

Theorem

The following formula holds: $$\int_a^b f(t) g^{\Delta}(t) \Delta t = (fg)(b) - (fg)(a) - \int_a^b f^{\Delta}(t) g(\sigma(t)) \Delta t,$$ where $\int$ denotes the delta integral.

Proof

See also

Integration by parts for delta integrals with sigma in integrand

References