   Chapter 4.R, Problem 9CC

Chapter
Section
Textbook Problem

# State the Substitution Rule. In practice, how do you use it?

To determine

To state:

a) The substitution rule

b)How do we use it in practice

Explanation

a)Substitution rule:

If u=g(x) is a differentiable function whose range is an interval I, and f is continuous on I, then

fgxg'xdx=f(u)du

b)In practice, substitute u=g(x) and du=g'(x) in the integrand to simplify a relatively complicated integral to a simpler integral. This is accomplished by changing from the original variable x to a new variable u that is a function of x

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