Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 16: Integrals and Vector Fields - Practice Exercises - Page 1028: 4



Work Step by Step

We calculate the line integral by using substitution as follows: $$ ds=\sqrt {(\dfrac{dx}{dt})^2+(\dfrac{dy}{dt})^2+(\dfrac{dz}{dt})^2} dt\\ =\sqrt {t^2} dt \\= t \space dt $$ $$\int_C f(x,y) ds=\int_{0}^{\sqrt 3} \sqrt {(1+t^2)} t \space dt \\= (\dfrac{1}{3})[(1+t^2)^{3/2}]_{0}^{\sqrt 3} \\=\dfrac{7}{3}$$
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