Limits of integration

Definition

Limits of integration are the values that define the interval over which a definite integral is evaluated. They are typically represented as the lower limit $a$ and the upper limit $b$ in the integral notation $\int_{a}^{b}$.

5 Must Know Facts For Your Next Test

1. The limits of integration determine the boundaries of the area under the curve being calculated.
2. Changing the limits of integration changes the value of the definite integral.
3. If the limits of integration are equal, i.e., $a = b$, then the value of the definite integral is zero.
4. Swapping the limits of integration ($\int_{a}^{b}$ vs. $\int_{b}^{a}$) results in negating the value of the integral.
5. Properly setting up and evaluating integrals requires correctly identifying and applying these limits.

Review Questions

• What happens to the value of a definite integral if its upper and lower limits are swapped?
• How do you interpret an integral with equal upper and lower limits?
• Why is it important to correctly identify and apply limits of integration when calculating a definite integral?

Related terms

Definite Integral: The evaluation of an integral with specific upper and lower bounds, giving a numerical result representing area under a curve.

Indefinite Integral: An antiderivative or primitive function representing a family of functions, without specific bounds.

$dx$: $dx$ denotes an infinitesimally small change in x, serving as part of differential notation in integrals.