5_5 - Section 5.5: The Substitution Rule Instructor: Ms....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 5.5: The Substitution Rule Instructor: Ms. Hoa Nguyen (nguyen@scs.fsu.edu) The Substitution Rule The idea behind the Substitution Rule is to replace a relatively complicated integral with a simpler integral by changing from one variable to another. Suppose we want to evaluate R f ( x ) dx which cannot be evaluated from the formulas in the previous sections. The Substitution Rule suggests to change from the variable x to a new variable u in the following steps: Let u = g ( x ) ( g ( x ) is a differentiable function whose range is a domain of f ). Try choosing g ( x ) to be some part of the integrand f ( x ). Then the differential of u is du = g 0 ( x ) dx . Substitute f ( x ) dx by u and du , if possible. In other words, R f ( g ( x )) g 0 ( x ) dx = R f ( u ) du . Otherwise, try a new substitution. After evaluating the new integral as a function of u , we need to replace u by g ( x ) to return to the original variable x . Remark
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.

Page1 / 2

5_5 - Section 5.5: The Substitution Rule Instructor: Ms....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online