Dummy variable

Definition

A dummy variable is a placeholder variable used in integration to represent the variable of integration. It has no impact on the final value of the definite integral.

5 Must Know Facts For Your Next Test

1. The choice of a dummy variable does not affect the result of the definite integral.
2. Common symbols for dummy variables include $x$, $t$, or $u$.
3. Dummy variables are essential for expressing integrals, especially when dealing with substitution.
4. In a double integral, different dummy variables may be used for each level of integration to avoid confusion.
5. When changing the order of integration in multiple integrals, it’s often necessary to change the dummy variables.

Review Questions

• Why is it called a 'dummy' variable?
• Does changing the dummy variable from $x$ to $u$ affect the value of an integral?
• Can you provide an example where using different dummy variables is helpful in solving an integral?

Related terms

Definite Integral: Represents the signed area under a curve within a specified interval.

Substitution: A method used in integration that involves changing variables to simplify an integral.

$\int_{a}^{b} f(x) \, dx$: Notation for a definite integral which calculates the area under function $f(x)$ from $a$ to $b$.