CALCULUS Understanding Its Concepts and Methods

Fundamental theorem of calculus

Fundamental theorem of calculus, first
form:If
*f*
is continuous on
[*a*,*b*]
then the function
*g*
defined by
is
continuous on
[*a*,*b*]
and
*g'*(*x*) = *f*(*x*)
for each
*x*
in the open interval
(*a*,*b*).

Fundamental theorem of calculus, second
form: If
*f*
is continuous on
[*a*,*b*],
and
*f = F'*,
then

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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.