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Definite Integral

Definite Integral

An integral which is evaluated over an interval. A definite integral is written Definite integral notation: integral from a to b of f(x)dx, where a and b are the lower and upper bounds of integration.. Definite integrals are used to find the area between the graph of a function and the x-axis. There are many other applications.

Formally, a definite integral is the limit of a Riemann sum as the norm of the partition approaches zero. That is, Definite integral formula: integral from a to b of f(x)dx equals limit as n→∞ of sum from k=1 to n of f(c_k)(x_k − x_{k−1}).

 

Example: definite integral from 2 to 5 of x² dx = (1/3)x³ evaluated from 2 to 5 = (1/3)(5)³ − (1/3)(2)³ = 117/3 = 39

 

 

See also

Fundamental Theorem of Calculus, integration methods, integral rules, work, volume by parallel cross-sections, disk method, cylindrical shell method