Definite Integrals

AP Calculus · Axiom Academy

Computing exact areas using the limit of Riemann sums From Approximation to Exact Area Definition: The Definite Integral This limit, when it exists, gives the signed area between f(x) and the x -axis from x = a to x = b . Area above the x -axis counts as positive; area below counts as negative. Properties of Definite Integrals The definite integral gives signed area (net area) Definite integrals have numbers as limits and produce a number The properties let you break integrals into simpler pieces

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