Skip over navigation

Definite Integral

Terms

Introduction and Summary

Definition of the Definite Integral

Antiderivative  -  An antiderivative of a function f (x) is a function F(x) such that F'(x) = f (x) .
Definite Integral  -  The limit approached by the n th upper and lower Riemann sums as n→∞ .
Integrable  -  The property that the definite integral of a function exists; that is, the upper and lower Riemann sums converge to the same value as the size of the approximating rectangles shrinks to zero.
Riemann Sum  -  The sum of areas of rectangles approximating the area under the graph of a function; examples include the upper and lower Riemann sums.
Fundamental Theorem of Calculus  -  The relationship between differentiation and integration:


F'(x)dx   = F(b) - F(a)  
f (t)dt   = f (x)  

Lower Riemann Sum  -  An approximation to the area below the graph of a function, equal to the total area of a number of thin rectangles inscribed in the region below the graph.
Upper Riemann Sum  -  An approximation to the area below the graph of a function, equal to the total area of a number of thin rectangles containing the region below the graph.
Telescoping Limits  -  The following property of the definite integral:

f (x)dx + f (x)dx = f (x)dx    

Follow Us