Change of variables

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

1. The substitution method requires selecting a new variable $u$ that simplifies the integral.
2. You must compute $du$ by differentiating $u$ with respect to the original variable.
3. After substituting $u$, you rewrite the entire integral in terms of $u$ and $du$.
4. Once you integrate with respect to $u$, you must substitute back the original variable.
5. A common choice for substitution involves recognizing parts of the integrand that resemble derivatives.

Review Questions

• How do you choose an appropriate substitution for an integral?
• What steps are involved in changing variables for integration?
• Why is it necessary to substitute back the original variable after integrating?

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.