Explain the connection between the chain rule for differentiation and the method of u-substitution for integration.

Chain rule: , u-Substitution:

Step-by-step explanation:

Differentiation and integration are reciprocal to each other. The chain rule indicate that a composite function must be differentiated, describing an inductive approach, whereas u-substitution allows integration by simplifying the expression in a deductive manner. That is:

Let integrate both sides in terms of x:

This result indicates that f must be rewritten in terms of u and after that first derivative needs to be found before integration.

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step-by-step explanation: