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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![**Problem Statement:**
Given the velocity function \( v(t) = 6t^2 - 3t \) on the interval \([3, 5]\), determine the displacement over this interval.
**Question:**
What is the displacement on \([3, 5]\)?
1. 160
2. 165
3. 170
4. 172
**Explanation:**
To find the displacement, we need to integrate the velocity function \( v(t) \) over the interval \([3, 5]\). The displacement \( \Delta x \) over the interval \([a, b]\) is given by:
\[ \Delta x = \int_{a}^{b} v(t) \, dt \]
In this case, \( a = 3 \) and \( b = 5 \). Calculate the integral of \( v(t) = 6t^2 - 3t \) from 3 to 5 to find the displacement.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5fb4dfc3-db65-4bb6-9a5b-9427f46c7a3d%2Fa1fed031-458d-4eab-8df8-b9b4570a87d8%2Fnce12ag_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given the velocity function \( v(t) = 6t^2 - 3t \) on the interval \([3, 5]\), determine the displacement over this interval.
**Question:**
What is the displacement on \([3, 5]\)?
1. 160
2. 165
3. 170
4. 172
**Explanation:**
To find the displacement, we need to integrate the velocity function \( v(t) \) over the interval \([3, 5]\). The displacement \( \Delta x \) over the interval \([a, b]\) is given by:
\[ \Delta x = \int_{a}^{b} v(t) \, dt \]
In this case, \( a = 3 \) and \( b = 5 \). Calculate the integral of \( v(t) = 6t^2 - 3t \) from 3 to 5 to find the displacement.
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