Variable of integration

Definition

A variable of integration is the variable with respect to which an integral is computed. It is typically represented as 'dx' in the integral notation.

5 Must Know Facts For Your Next Test

1. The variable of integration indicates the variable over which the function is being integrated.
2. In a definite integral, the limits of integration are applied to this variable.
3. Changing the variable of integration can simplify or otherwise change the computation of an integral.
4. The differential element, such as 'dx,' 'dy,' etc., must match the integrand's variable for proper evaluation.
5. In multiple integrals, each variable has its own differential element and limits.

Review Questions

• What does the variable of integration signify in an integral?
• How does changing the variable of integration affect an integral?
• Why must the differential element match the integrand's variable?

Related terms

Integrand: The function that is being integrated in an integral.

Definite Integral: $\int_{a}^{b} f(x) \, dx$ represents the area under $f(x)$ from $x=a$ to $x=b$.

Indefinite Integral: $\int f(x) \, dx$ represents a family of functions differing by a constant.