What is the Purpose of U Substitution in Solving Integrals?

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SUMMARY

The discussion focuses on the application of U substitution in solving the integral of 1/(1-y)dy. The correct solution involves recognizing that substituting 1-y with U simplifies the integral to -∫(1/u)du, which is a standard integral yielding ln|u| + C. The participant highlights the importance of maintaining the negative sign during substitution, emphasizing that while U substitution is beneficial, the integral can also be solved directly due to its simplicity.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with U substitution method
  • Knowledge of logarithmic functions
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the U substitution method in detail
  • Practice solving integrals using U substitution with various functions
  • Explore the properties of logarithmic integrals
  • Review common mistakes in integral calculus, particularly with sign errors
USEFUL FOR

Students learning calculus, educators teaching integral calculus, and anyone seeking to improve their skills in solving integrals using substitution methods.

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Homework Statement




the integral of 1/(1-y)dy

Homework Equations





The Attempt at a Solution



ln|1-y|+C

however I believe you use u substitution as 1-y=U? Why is this so?


 
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You lost a minus sign in your solution. Making a substitution would work because the integral would reduce to
[tex]\int{-\frac{1}{u}du}[/tex]
which is well known, but this example is simple enough that you could solve it just by looking at it.
 

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