Limits of integration

Limits of integration are the endpoints that specify the interval over which a definite integral is evaluated. They determine the domain of accumulation and the orientation of the integral.

Definite integral: A number representing the signed accumulation of a function over an interval. Its endpoints are the limits of integration.
Fundamental theorem of calculus: The theorem connecting definite integrals to antiderivatives and derivatives. It evaluates an integral by subtracting antiderivative values at the two limits.
Area between curves: The area enclosed between two curves over a specified interval. The limits identify the horizontal span over which the area is accumulated.
Indefinite integral: The family of antiderivatives of a function, written without specified endpoints. Unlike a definite integral, it has no limits selecting an interval or a numerical value.
Interval (mathematics): A set of real numbers containing every number between any two of its elements. The integration limits delimit the interval being evaluated.
Reversing the limits of integration: The identity that swapping a definite integral's endpoints changes its sign. It makes endpoint order encode the integral's orientation.
Disk integration method: A method for finding a solid's volume by integrating the areas of circular cross-sections. Its bounds mark the extent of the solid along the axis of slicing.
Contour integral: An integral evaluated along an oriented curve in the complex plane or another space. Its path, rather than two real interval endpoints alone, specifies where integration occurs.
Integral notation: The symbolic conventions used to write integrals, including the integral sign, integrand, variable, and bounds. The limits appear as upper and lower indices beside the integral sign.
Change of variables: A method for transforming an integral by substituting a new variable and adjusting the integrand and bounds. A substitution transforms both limits to the corresponding values of the new variable.

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Iterated integralRelated: Variable-dependent limits encode how slices of the region change across variables.