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Antiderivative
An antiderivative of a function f (x) is a function F(x) such that F'(x) = f (x).
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Definite Integral
The limit approached by the nth upper and lower Riemann sums as n→∞.
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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.
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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.
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Fundamental Theorem of Calculus
The relationship between differentiation and integration:
F'(x)dx= F(b) - F(a) 
f (t)dt
= f (x)
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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.
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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.
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Telescoping Limits
The following property of the definite integral:
f (x)dx + 
f (x)dx = 
f (x)dx
