Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 7, Problem 1PE
To determine
The method of
Expert Solution & Answer
Explanation of Solution
The method of integration by substitution or change of variables is based on the chain rule for derivatives.
The method
The steps for using substitution for integration for indefinite integral are given below.
- Calculate the derivative of u and solve it for it for dx .
- Substitute the expression for u and dx in the original integral.
- Eliminate the variable x and leave the integral in u only.
- Simplify the integral.
- Integrate the integral.
- Again, substitute the value of u in the expression.
The steps for using substitution for solving a definite integral are same but the limits of the integration are also needed to changed according to the substitution.
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Students have asked these similar questions
The spread of an infectious disease is often modeled using the following autonomous differential equation:
dI
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dt
where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of
transmission, and μ is the rate at which people recover from infection.
Close
a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria.
b) (5 points) For the equilbria in part a), determine whether each is stable or unstable.
c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the
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d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.
Find the indefinite integral.
Check
Answer:
7x
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show sketch
Chapter 7 Solutions
Calculus
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