Which technique is commonly used to evaluate integrals?

The technique of indefinite substitution is a fundamental method used to evaluate integrals, particularly when dealing with integrals that involve straightforward compositions of functions. This approach transforms a complex integral into a simpler one by making a substitution for a part of the integrand, which allows the integration process to become more manageable.

For instance, if you have an integral involving a function and its derivative, performing an indefinite substitution can significantly simplify the problem. By substituting a new variable for the part of the integrand that complicates the process, you can often directly apply basic antiderivative rules to find the integral.

Indefinite substitution is widely applicable in various scenarios, particularly where the integral can be transformed to match a known form or basic integral. It's essential for learning integration techniques, as it establishes a foundation for more complex techniques like integration by parts or trigonometric substitution.

The other techniques mentioned, such as definite integration, deal with finding the specific area under the curve between two bounds but are not a method for evaluating general integrals in the same way. Partial differentiation pertains more to functions of multiple variables rather than the evaluation of integrals. Area approximation, while useful in estimating integrals, does not yield an exact integral value in the same manner as indefinite