Book Problem 13 Find the length L of the arc formed by y = ln (secx), 0≤ x ≤ π/3. L = f/³√√1+ (f'(x))² da where f'(x) = L = f/3√(g(x))² dx where g(x) = Now use the Table of Integrals at the end of your book to evaluate L: Formula number and the length L of the curve M
Book Problem 13 Find the length L of the arc formed by y = ln (secx), 0≤ x ≤ π/3. L = f/³√√1+ (f'(x))² da where f'(x) = L = f/3√(g(x))² dx where g(x) = Now use the Table of Integrals at the end of your book to evaluate L: Formula number and the length L of the curve M
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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![**Book Problem 13**
Find the length L of the arc formed by \( y = \ln(\sec x) \), \( 0 \leq x \leq \pi/3 \).
\[ L = \int_{0}^{\pi/3} \sqrt{1 + \left( f'(x) \right)^2} \, dx \text{ where } f'(x) = \boxed{\phantom{x}}. \]
\[ L = \int_{0}^{\pi/3} \sqrt{\left( g(x) \right)^2} \, dx \text{ where } g(x) = \boxed{\phantom{x}}. \]
Now use the Table of Integrals at the end of your book to evaluate L:
Formula number \( \boxed{\phantom{x}} \) and the length L of the curve \( = \boxed{\phantom{x}}. \)
**Explanation:**
- The given problem is about finding the arc length of the function \( y = \ln(\sec x) \) over the interval \( 0 \leq x \leq \pi/3 \).
- There are two integral representations provided for calculating \( L \):
1. Using the general arc length formula that involves the square root of \( 1 + \left( f'(x) \right)^2 \).
2. Using a form involving \( g(x) \), which potentially simplifies the calculation.
The placeholders (boxed areas) are meant for identifying the derivative \( f'(x) \), a simplified function \( g(x) \), the formula number from the integral table, and the final arc length \( L \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61ed9ec8-c9ca-4552-b8a2-44c86eb99b07%2Fb31e9697-53c0-4f37-8f7d-4484ba2cbad2%2F05q7mve_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Book Problem 13**
Find the length L of the arc formed by \( y = \ln(\sec x) \), \( 0 \leq x \leq \pi/3 \).
\[ L = \int_{0}^{\pi/3} \sqrt{1 + \left( f'(x) \right)^2} \, dx \text{ where } f'(x) = \boxed{\phantom{x}}. \]
\[ L = \int_{0}^{\pi/3} \sqrt{\left( g(x) \right)^2} \, dx \text{ where } g(x) = \boxed{\phantom{x}}. \]
Now use the Table of Integrals at the end of your book to evaluate L:
Formula number \( \boxed{\phantom{x}} \) and the length L of the curve \( = \boxed{\phantom{x}}. \)
**Explanation:**
- The given problem is about finding the arc length of the function \( y = \ln(\sec x) \) over the interval \( 0 \leq x \leq \pi/3 \).
- There are two integral representations provided for calculating \( L \):
1. Using the general arc length formula that involves the square root of \( 1 + \left( f'(x) \right)^2 \).
2. Using a form involving \( g(x) \), which potentially simplifies the calculation.
The placeholders (boxed areas) are meant for identifying the derivative \( f'(x) \), a simplified function \( g(x) \), the formula number from the integral table, and the final arc length \( L \).
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