Category:Examples of Use of Integration by Parts

This category contains examples of use of Integration by Parts.

Let $f$ and $g$ be real functions which are continuous on the closed interval $\closedint a b$.

Let $f$ and $g$ have primitives $F$ and $G$ respectively on $\closedint a b$.

Then:

Primitive

$\ds \int \map f t \map G t \rd t = \map F t \map G t - \int \map F t \map g t \rd t$

on $\closedint a b$.

Definite Integral

$\ds \int_a^b \map f t \map G t \rd t = \bigintlimits {\map F t \map G t} a b - \int_a^b \map F t \map g t \rd t$

This technique is called integration by parts.