Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 9 - Further Applications of the Integral and Taylor Polynomials - 9.1 Arc Length and Surface Area - Exercises - Page 468: 2



Work Step by Step

To find the arc length $s$ of the curve $y= \tan x$ between $x=0$ and $x=\pi/4$, we fist calculate $y'=\sec^2 x$. Then we have the integral, $$s=\int_0^{\pi/4}\sqrt{1+(y')^2}dx=\int_0^{\pi/4}\sqrt{1+\sec^4}dx.$$
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