Method of strategic substitution

Definition

Method of strategic substitution involves replacing a complex expression with a simpler one to facilitate integration. This technique often simplifies the problem, making it easier to solve.

5 Must Know Facts For Your Next Test

1. Strategic substitution is commonly used to simplify integrands before applying partial fractions.
2. This method can be particularly useful when dealing with rational functions.
3. Substitution might involve setting $u$ equal to a polynomial or another expression within the integrand.
4. After substitution, the resulting integral should be easier to integrate using standard techniques.
5. Reverting the substituted variable back to the original variable is crucial for arriving at the final answer.

Review Questions

• What is the purpose of using strategic substitution in integration problems?
• How do you choose an appropriate substitution for simplifying an integrand?
• Why is it important to revert back to the original variable after performing a substitution?

Related terms

Partial Fractions: A method used to decompose rational functions into simpler fractions that are easier to integrate.

Integration by Substitution: A technique where a new variable replaces part of an integrand, simplifying its structure.

$u$-Substitution: $(u)$-Substitution is another term for integration by substitution, where $u$ represents the new variable.