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: 6


The integral converges to $19$.

Work Step by Step

Recall the convergence/divergence rules for "p-integrals" on page 439. Since $ p= \frac{20}{19}>1$, the integral converges. $$\int_1^\infty \frac{dx}{x^{20/19}}=\lim\limits_{R \to \infty}\int_1^R\frac{dx}{x^{20/19}}\\=\lim\limits_{R \to \infty} \frac{1}{-1/19}x^{-1/19}|_1^R=-19\lim\limits_{R \to \infty}(\frac{1}{R^{1/19}}-1)=19.$$
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