Find the mass of the thin bar with the given density function. p(x) = 1+ sin x; for sxs Set up the integral that gives the mass of the thin bar. dx (Type exact answers.)
Find the mass of the thin bar with the given density function. p(x) = 1+ sin x; for sxs Set up the integral that gives the mass of the thin bar. dx (Type exact answers.)
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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![**Finding the Mass of a Thin Bar Using a Density Function**
To determine the mass of a thin bar with a given density function, use the following function:
\[ \rho(x) = 1 + \sin x \]
This function is defined over the interval:
\[ \frac{\pi}{6} \leq x \leq \frac{\pi}{4} \]
**Objective:**
Set up the integral that calculates the mass of the thin bar.
**Integral Setup:**
\[
\int_{\frac{\pi}{6}}^{\frac{\pi}{4}} (1 + \sin x) \, dx
\]
**Instructions:**
- Ensure the function \(\rho(x)\) and the limits of integration are correctly placed in the integral setup.
- Type your answer in exact terms.
The problem involves setting up an integral with the given bounds to find the mass. There's no graph or diagram associated with the problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b64ac97-c6ea-4a6a-9afb-fb0dadf017bd%2Fa9a286f4-e7b8-4ac6-b12b-edeedc25d714%2Fcmy2jh_processed.png&w=3840&q=75)
Transcribed Image Text:**Finding the Mass of a Thin Bar Using a Density Function**
To determine the mass of a thin bar with a given density function, use the following function:
\[ \rho(x) = 1 + \sin x \]
This function is defined over the interval:
\[ \frac{\pi}{6} \leq x \leq \frac{\pi}{4} \]
**Objective:**
Set up the integral that calculates the mass of the thin bar.
**Integral Setup:**
\[
\int_{\frac{\pi}{6}}^{\frac{\pi}{4}} (1 + \sin x) \, dx
\]
**Instructions:**
- Ensure the function \(\rho(x)\) and the limits of integration are correctly placed in the integral setup.
- Type your answer in exact terms.
The problem involves setting up an integral with the given bounds to find the mass. There's no graph or diagram associated with the problem.
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