Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 7 - Techniques of Integration - 7.8 Improper Integrals - 7.8 Exercises: 2

Answer

B , C, and D

Work Step by Step

if the domain or range of the integrated portion approach infinity then it is an improper integral (a) the domain and range never approach infinity. this can be seen by graphing it (b) $\lim\limits_{x \to \pi/2}$ tan(x) = $\infty$ the range goes to $\infty$therefore B is improper.(optional:graph to double check.) (c) $\lim\limits_{a \to -1}$ = $\infty$ the range goes to $\infty$ therefore C is improper.(optional:graph to double check.) (d) the domain goes to $\infty$ therefore D is improper.(optional:graph to double check.)
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