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Mastering Integration by Substitution: A Comprehensive Guide

Understand the intricacies of Integration by Substitution technique to solve a variety of functions. Learn how to change variables, rewrite functions, and integrate them effectively, with step-by-step examples for better comprehension. Explore the nuances of definite integrals and the importance of using correct limits in the process.

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Mastering Integration by Substitution: A Comprehensive Guide

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  1. Integration bySubstitution

  2. The chain rule allows us to differentiate a wide variety of functions, but we are able to find antiderivatives for only a limited range of functions? We can sometimes use substitution or change of variable to rewrite functions in a form that we can integrate.

  3. The technique is a little different for definite integrals. new limit new limit Example 7: We can find new limits, and then we don’t have to substitute back. We could have substituted back and used the original limits.

  4. Leave the limits out until you substitute back. This is usually more work than finding new limits Example 7 continued: Using the original limits: Wrong! The limits don’t match!

  5. Example 8: Don’t forget to use the new limits.

  6. Acknowledgement I wish to thank Greg Kelly from Hanford High School, Richland, USA for his hard work in creating this PowerPoint. http://online.math.uh.edu/ Greg has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum. Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au p

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