Variable of integration

Definition

The variable of integration is the symbol used to represent the variable with respect to which an integral is being evaluated. It appears in the differential element, such as $dx$, within an integral expression.

5 Must Know Facts For Your Next Test

1. The variable of integration must match the differential element in the integral expression.
2. Changing the variable of integration can transform an integral into a simpler or more solvable form.
3. In definite integrals, the limits of integration are associated with the variable of integration.
4. When performing substitution in integrals, a new variable of integration often replaces the original one.
5. The choice of variable of integration does not affect the value of a definite integral as long as limits are adjusted accordingly.

Review Questions

• Why must the differential element match the variable of integration?
• How does changing the variable of integration help simplify an integral?
• What happens to the limits of integration when you change the variable of integration?

Related terms

Definite Integral: An integral evaluated over a specific interval, producing a numerical value corresponding to the area under a curve between two points.

Change of Variable: A method used to simplify an integral by substituting a new variable for an existing one.

$u$-Substitution: $u$-Substitution is a technique for simplifying integrals by substituting part of an integrand with a single variable $u$ and adjusting differential elements accordingly.