{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 5_5 - Section 5.5 The Substitution Rule Instructor Ms Hoa...

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

Section 5.5: The Substitution Rule Instructor: Ms. Hoa Nguyen 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 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 ( x ) dx . Substitute f ( x ) dx by u and du , if possible. In other words, f ( g ( x )) g ( x ) dx = 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 : The main challenge in using the rule is to think of an appropriate substitution.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

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

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

View Full Document
Ask a homework question - tutors are online