Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
Definition
Change of variables, also known as substitution, is a method used to simplify the process of finding integrals. It involves replacing the original variable with a new variable to make integration more manageable.
5 Must Know Facts For Your Next Test
The substitution method requires selecting a new variable $u$ that simplifies the integral.
You must compute $du$ by differentiating $u$ with respect to the original variable.
After substituting $u$, you rewrite the entire integral in terms of $u$ and $du$.
Once you integrate with respect to $u$, you must substitute back the original variable.
A common choice for substitution involves recognizing parts of the integrand that resemble derivatives.
Review Questions
Related terms
Integral: The result of integrating a function, representing area under a curve or accumulation of quantities.
$u$-Substitution: A specific type of change of variables where a part of the integrand is replaced by a single variable $u$.
Definite Integral: An integral evaluated over a specific interval, resulting in a numerical value.