PrepZii

table

Basic Definite Integral Properties

The opening properties cover dummy variables, reversal of limits, interval splitting, and the $a+b-x$ transformation.

Property	Formula
Dummy variable	$\int_a^b f(x)\,dx=\int_a^b f(t)\,dt$
Reversing limits	$\int_a^b f(x)\,dx=-\int_b^a f(x)\,dx$
Interval splitting	$\int_a^b f(x)\,dx=\int_a^c f(x)\,dx+\int_c^b f(x)\,dx$
Transformation	$\int_a^b f(x)\,dx=\int_a^b f(a+b-x)\,dx$

$a$

constant or limit

$b$

constant or limit

$f$

function