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Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The problem presented is an integral calculus question. It asks to find the indefinite integral of the function \( \frac{4}{x} \) with respect to \( x \). ### Problem Statement Find \( \int \frac{4}{x} \, dx \). ### Explanation To solve this integral, you use the basic integration rule for \( \frac{1}{x} \), which is \( \int \frac{1}{x} \, dx = \ln |x| + C \), where \( C \) is the constant of integration. Since there is a constant multiplier of 4, it can be factored out of the integral: \[ \int \frac{4}{x} \, dx = 4 \int \frac{1}{x} \, dx = 4 \ln |x| + C \] ### Final Solution The indefinite integral of the function is: \[ 4 \ln |x| + C \]
Transcribed Image Text:The problem presented is an integral calculus question. It asks to find the indefinite integral of the function \( \frac{4}{x} \) with respect to \( x \). ### Problem Statement Find \( \int \frac{4}{x} \, dx \). ### Explanation To solve this integral, you use the basic integration rule for \( \frac{1}{x} \), which is \( \int \frac{1}{x} \, dx = \ln |x| + C \), where \( C \) is the constant of integration. Since there is a constant multiplier of 4, it can be factored out of the integral: \[ \int \frac{4}{x} \, dx = 4 \int \frac{1}{x} \, dx = 4 \ln |x| + C \] ### Final Solution The indefinite integral of the function is: \[ 4 \ln |x| + C \]
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