What technique is used to simplify integrals by replacing parts of the function?

Integration by substitution is a technique that simplifies integrals by replacing parts of the function with a new variable, making the integral easier to evaluate. This process often involves identifying a part of the integrand that can be substituted with a single variable, which transforms the integral into a more manageable form. The substitution is usually chosen to simplify the integrand, leading to a more straightforward integration process.

For example, if you had an integral involving a complicated expression, you might let a new variable represent a portion of that expression. After performing the integral in terms of the new variable, you can convert it back to the original variable, completing the integration process.

In contrast, the other techniques mentioned serve different purposes. The method of partial integration, for instance, is used to integrate products of functions, while the trapezoidal and Simpson's rules are numerical methods for approximating integrals rather than analytic techniques for simplifying and calculating them directly. Therefore, integration by substitution stands out as the correct choice for the technique that simplifies integrals by replacing parts of the function.