University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson

Chapter 8 - Section 8.7 - Improper Integrals - Exercises - Page 471: 2

Answer

$1000$

Work Step by Step

Consider $f(x)=\int_{1}^{\infty} \dfrac{1}{x^{1.001}} dx$ $\lim\limits_{a \to \infty} f(x)= \lim\limits_{a \to \infty}\int_{1}^{a}\dfrac{1}{x^{1.001}} dx=\lim\limits_{a \to \infty} [\dfrac{-x^{1.001}}{0.001}]_{1}^{a}$ or, $\lim\limits_{a \to \infty} [-1000a^{-0.001}+1000]= 1000$

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