CALCULUS Understanding Its Concepts and Methods

Area function

The area
function of a positive-valued function *f* on an interval [*a*, *b*] is the
area of the region bounded by the graph of *f*, the interval [*a*, *x*] , and the vertical lines
through *a *and *x*. It is denoted
and is an antiderivative of *f*.
In the animated figure, *A*
(*x*) is the area of the
shaded region as *x*
increases from *a* to *b*.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.