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 - Preliminary Questions - Page 468: 1



Work Step by Step

To find the length of the curve $y=\cos x$, we fist calculate $y'=-\sin x$. Then we have the integral, $$\int_0^{\pi/4}\sqrt{1+(y')^2}dx=\int_0^{\pi/4}\sqrt{1+\sin^2x}dx.$$ So the right answer is $$\int_0^{\pi/4}\sqrt{1+\sin^2x}dx.$$
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