Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Section 5.3 - The Fundamental Theorem of Calculus - 5.3 Exercises - Page 400: 57


The integral does not exist.

Work Step by Step

$\int_{\pi/3}^{\pi} sec~\theta~tan~\theta~d\theta = \int_{\pi/3}^{\pi} \frac{sin~\theta}{cos^2~\theta}~d\theta$ The graph of $~~\frac{sin~\theta}{cos^2~\theta}~~$ has a vertical asymptote at the point $\theta=\frac{\pi}{2}$. Therefore, the function is not continuous on the interval $[\frac{\pi}{3},\pi]$ and we can not apply the Fundamental Theorem to calculate the value of this integral. The integral does not exist.
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