Find indicated. are length interval of the graph of the function over y = In (9 cos(x)), 0≤ x ≤ 11. Keep 4 decimals.
Find indicated. are length interval of the graph of the function over y = In (9 cos(x)), 0≤ x ≤ 11. Keep 4 decimals.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![# Educational Text on Calculus Problem Solving
## Problem 3
Use the shell method to set up and evaluate the integral that gives the volume of solid generated by revolving the plane region bounded by:
\[ y = 9x, \quad y = 18, \quad x = 0 \]
about the y-axis.
---
## Problem 4
Find the arc length of the graph of the function over the indicated interval:
\[ y = \ln(9\cos(x)), \quad 0 \leq x \leq \frac{\pi}{4} \]
*Keep 4 decimals.*
---
### Explanation
**Problem 3:**
The shell method involves using cylindrical shells to find the volume of a solid of revolution. The setup requires integrating along the x-axis, using the given boundaries to define the range and height of the shells.
**Problem 4:**
This involves calculating the arc length of a curve over a specified interval. The function given, \( y = \ln(9\cos(x)) \), is bounded from \( x = 0 \) to \( x = \frac{\pi}{4} \). Calculating arc length involves integrating the square root of 1 plus the derivative of the function squared over the interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe35298e5-10ed-452c-b18c-35d9ef29ce25%2F8b6a5eb3-077a-4e33-816f-3e893852579a%2Fa8copqk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Educational Text on Calculus Problem Solving
## Problem 3
Use the shell method to set up and evaluate the integral that gives the volume of solid generated by revolving the plane region bounded by:
\[ y = 9x, \quad y = 18, \quad x = 0 \]
about the y-axis.
---
## Problem 4
Find the arc length of the graph of the function over the indicated interval:
\[ y = \ln(9\cos(x)), \quad 0 \leq x \leq \frac{\pi}{4} \]
*Keep 4 decimals.*
---
### Explanation
**Problem 3:**
The shell method involves using cylindrical shells to find the volume of a solid of revolution. The setup requires integrating along the x-axis, using the given boundaries to define the range and height of the shells.
**Problem 4:**
This involves calculating the arc length of a curve over a specified interval. The function given, \( y = \ln(9\cos(x)) \), is bounded from \( x = 0 \) to \( x = \frac{\pi}{4} \). Calculating arc length involves integrating the square root of 1 plus the derivative of the function squared over the interval.
Expert Solution
Step 1
The arc length of the curve: in the domain: is calculated using the formula: .
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