To find a function when its derivative is known, we employ the reverse process of differentiation, termed anti-derivation or integration. This involves the use of differentials of variables, particularly in the method of substitution during the integration process. Before delving further into anti-derivation, let’s first explore differentials of variables.
Differentials of Variables Integration serves as the inverse of differentiation. In Chapter 2, we focused on finding the derived function of a given function. Now, we consider the opposite process — determining a function when its derivative is known.
Integration as Anti-Derivative (Inverse of Derivative): The inverse process of differentiation, seeking a function when its derivative is given, is termed anti-differentiation or integration.
Exercise 3.1
Exercise 3.2
Exercise 3.3
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Exercise 3.4
Exercise 3.5
Exercise 3.6
Exercise 3.7
Exercise 3.8