# Integration by parts for delta integrals with no sigma in integrand

From timescalewiki

## 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