Calculus Study Guide and Solutions Manual: Step-by-Step Solutions to Calculus Problems by David McMahon

Author:David McMahon [McMahon, David]
Language: eng
Format: azw3
Publisher: Bluewater Publishing LLC
Published: 2014-01-22T05:00:00+00:00



If the limits of integration are changed, the sign of the integral changes. Make a note of the following



Also make a notational note. If is the antiderivative of , we sometimes indicate the limits at which the integral is to be evaluated at with the following notation



So, for example, if you see



this means



And



Example 5-25

Apply the first fundamental theorem of calculus to find



Solution

The functionis not elementary and so can’t be integrated immediately. We can do this using u-substitution, a technique that can be used with definite integrals as well. Notice that if , then . When applying u-substitution to a definite integral, we must change the limits of integration as well. We do this using the relationship . The limits in this case are and . Now, when , then

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