Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 440: 2


(a) $$\int_1^Rx^{-4/3}dx= -3(R^{-1/3}-1).$$ (b) $$\int_1^\infty x^{-4/3}dx =3.$$

Work Step by Step

(a) $$\int_1^Rx^{-4/3}dx=\frac{1}{-1/3}x^{-1/3}|_1^R=-3(R^{-1/3}-1).$$ (b) $$\int_1^\infty x^{-4/3}dx=\lim\limits_{R \to \infty}\int_1^Rx^{-4/3}dx\\= -3\lim\limits_{R \to \infty}(R^{-1/3}-1)=-3(0-1)=3.$$
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