Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 5 - Integration - 5.3 Fundamental Theorem of Calculus - 5.3 Exercises: 90

Answer

$$1$$

Work Step by Step

$$\eqalign{ & \int_{\pi /4}^{\pi /2} {{{\csc }^2}\theta } d\theta \cr & {\text{integrate using the basic rules for integration}} \cr & = \left. {\left( { - \cot \theta } \right)} \right|_{\pi /4}^{\pi /2} \cr & {\text{using the fundamental theorem}} \cr & = - \left( {\cot \frac{\pi }{2} - \cot \frac{\pi }{4}} \right) \cr & {\text{simplify}} \cr & = - \left( {0 - 1} \right) \cr & = 1 \cr} $$
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