What is the purpose of substitution in integration?

Substitution in integration is primarily utilized to replace variables in the integral with new variables or expressions that simplify the integration process. This technique focuses on identifying a part of the integrand that can be substituted with a single variable, which often results in a simpler integral that is easier to solve.

For instance, if you have an integral that contains a composite function, substituting the inner function can reduce the complexity of the integral, making it possible to solve it using basic integration rules. Essentially, this process not only streamlines the computation but also helps in identifying integrals that might be difficult to tackle in their original form.

While changing the limits can be a part of the substitution process when dealing with definite integrals, the primary aim of substitution is simplification rather than limit adjustment. The option about using a calculator may relate to computational efficiency, but that is not the core purpose of substitution. Similarly, converting integrals into simpler algebraic forms is a consequence of substitution rather than its primary objective. Thus, the emphasis on simplifying calculations directly aligns with the purpose of substitution in integration.