U-Substitution
Definition
U-substitution is a technique used to simplify integrals by substituting a new variable for part of the original expression.
Analogy
Imagine you're at a party and there's one person who keeps causing trouble. To avoid dealing with them directly, you substitute them with someone else who behaves better. Similarly, in u-substitution, we substitute part of the original expression with a new variable to make it easier to integrate.
Related terms
Chain Rule: The chain rule is used in differentiation to find derivatives when there are nested functions.
Integration by Parts: Integration by parts is another integration technique that involves breaking down an integral into two parts and applying specific rules.
Trigonometric Substitutions: Trigonometric substitutions are special cases of u-substitution where trigonometric identities are used to simplify integrals involving trigonometric functions.
"U-Substitution" appears in:
Additional resources (2)
Practice Questions (6)
What is u-substitution?
When is u-substitution used?
Which of the following integrals would require u-substitution to solve?
Which of the following integrals would NOT require u-substitution to solve?
What part of the function in the integral ∫sqrt(3x+7)dx should u be set equal to in order to use a u-substitution to solve the integral?
Rewrite the integral ∫sqrt(3x+7)dx with an appropriate u-substitution.
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