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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Question
![**Integral Equation:**
\[
\int_{\log_{2}}^{x} \frac{1}{\sqrt{e^{x} - 1}} \, dx = \frac{\pi}{6}
\]
**Task:** Solve the equation.
---
**Explanation:**
This equation involves an integral with an upper limit of \(x\) and a lower limit of \(\log_{2}\). The integrand is \(\frac{1}{\sqrt{e^{x} - 1}}\). The goal is to find the value of \(x\) that satisfies this equation where the definite integral equals \(\frac{\pi}{6}\).
The left side represents the definite integral of the function \(\frac{1}{\sqrt{e^{x} - 1}}\) from \(\log_{2}\) to \(x\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd38580b4-df42-4772-882a-8d760db67d1c%2F7de73580-e14d-46f1-a60d-cfaf575807d8%2Fhq98f7l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Integral Equation:**
\[
\int_{\log_{2}}^{x} \frac{1}{\sqrt{e^{x} - 1}} \, dx = \frac{\pi}{6}
\]
**Task:** Solve the equation.
---
**Explanation:**
This equation involves an integral with an upper limit of \(x\) and a lower limit of \(\log_{2}\). The integrand is \(\frac{1}{\sqrt{e^{x} - 1}}\). The goal is to find the value of \(x\) that satisfies this equation where the definite integral equals \(\frac{\pi}{6}\).
The left side represents the definite integral of the function \(\frac{1}{\sqrt{e^{x} - 1}}\) from \(\log_{2}\) to \(x\).
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