Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
Definition
Change of variables is a method used to simplify integrals by substituting a new variable for an existing one. This technique often makes the integral easier to evaluate.
5 Must Know Facts For Your Next Test
The substitution $u = g(x)$ is commonly used, where $g(x)$ is a differentiable function.
After substitution, the differential $dx$ must be expressed in terms of the new variable: $du = g'(x) dx$.
The limits of integration must also be changed when dealing with definite integrals.
This method can help in evaluating integrals involving composite functions.
It's crucial to revert back to the original variable if solving an indefinite integral.
Review Questions
Related terms
Indefinite Integral: An integral without specified limits, representing a family of antiderivatives.
An integral with specified upper and lower limits, representing the net area under a curve.
$u$-Substitution: $u$-Substitution is a specific type of change of variables where $u = g(x)$ transforms an integral into one that is easier to evaluate.