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Fundamental Theorems of Calculus
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The concept that formalizes the intuitive notion of 'area under a curve' using a limit process.
Integration
A method for approximating the area under a function's graph.
Numerical Integration
The equation that represents the derivative of an antiderivative.
Derivative of an Antiderivative
The condition for being able to switch the order of integration and summation in a series.
Uniform Convergence
The theorem connecting the concept of the derivative of a function to the concept of the integral.
First Fundamental Theorem of Calculus
A process to evaluate the definite integral of a piecewise continuous function.
Integration of Piecewise Functions
The principle that allows one to differentiate under the integral sign when the integrand involves a parameter.
Leibniz's Rule
A technique involving swapping the order of integration in double integrals.
Fubini's Theorem
The term for reversing differentiation, finding a function whose derivative is the given function.
Antidifferentiation
The rule for integrating a sum of functions.
Linearity of Integration
The term describes the set of all antiderivatives of a function.
Indefinite Integral
The larger value in the definite integral notation, often interpreted as the end point in the interval of integration.
Upper Limit of Integration
The property stating that if a function is integrable on a closed interval, then its definite integral over that interval is a number.
Existence of Definite Integrals
The type of continuity required for a function to have an antiderivative on an interval.
Continuous Functions
The theorem used to compute the derivative of an integral as a function of its upper limit.
Second Fundamental Theorem of Calculus
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