Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 4 - Integration - 4.6 The Fundamental Theorem Of Calculus - Exercises Set 4.6 - Page 320: 18

Answer

$$1$$

Work Step by Step

$$\eqalign{ & \int_0^{\pi /4} {se{c^2}\theta } d\theta \cr & {\text{find antiderivative use integration formulas from table 4}}{\text{.2}}{\text{.1}} \cr & \int_0^{\pi /4} {se{c^2}\theta } d\theta = \left( {\tan \theta } \right)_0^{\pi /4} \cr & {\text{part 1 of fundamental theorem of calculus}} \cr & = \tan \left( {\frac{\pi }{4}} \right) - \tan \left( 0 \right) \cr & {\text{recall that tan}}\left( {\frac{\pi }{4}} \right) = 1{\text{ and tan}}\left( 0 \right) = 0 \cr & = 1 - 0 \cr & = 1 \cr & {\text{then}} \cr & \int_0^{\pi /4} {se{c^2}\theta } d\theta = 1 \cr} $$
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