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Fundamental Theorem of Calculus

Definition

The Fundamental Theorem of Calculus states that if f(x) is continuous on an interval [a, b] and F(x) is any antiderivative of f(x), then ∫[a,b] f(x) dx = F(b) - F(a). In simpler terms, it relates differentiation and integration by showing that finding the area under a curve can be done by evaluating its antiderivative at two points.

Related terms

Antiderivative: An antiderivative (also known as an indefinite integral) reverses differentiation and gives us back the original function before it was differentiated.

Definite Integral: A definite integral is used to find the exact area under a curve between two given points. It is represented by ∫[a,b] f(x) dx, where a and b are the limits of integration.

Riemann Sum: A Riemann sum is an approximation of the area under a curve using rectangles. It involves dividing the interval into subintervals and evaluating the function at specific points within each subinterval.

"Fundamental Theorem of Calculus" appears in:

Subjects (1)

  • AP Physics C: Mechanics

Study guides (2)

  • AP Calculus AB/BC - 6.14 Selecting Techniques for Antidifferentiation (AB)

  • AP Calculus AB/BC - 10.15 Representing Functions as Power Series

Additional resources (1)

  • AP Calculus AB/BC - Unit 6 Overview: Integration and Accumulation of Change

Practice Questions (1)

  • What is the fundamental theorem of calculus?

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Cram Mode

AP Score Calculators

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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.