Antiderivatives and Indefinite Integrals Modified by Mrs. King from Paul's Online Math Tutorials and Notes IndefiniteIntegrals.asp

Introduction In the past two chapters we’ve been given a function f(x) and asking what was the derivative of this function. We now want to turn things around and ask what function we differentiated to get the function f(x).

Example 1 What function did we differentiate to get the following function:

Process for finding an Antiderivative: This is the reverse of differentiation, so we are going to add one to the exponent and then divide by that new exponent.

Constants We know that the derivative of a constant is zero and any function of the form will result in the function f(x) upon differentiating.

Definitions Given a function f(x) an anti-derivative of f(x) is any function F(x) such that

Definitions If F(x) is any anti-derivative of f(x) then the most general anti-derivative of f(x) is called an indefinite integral and denoted

Definitions In this definition the ∫ is called the integral symbol, f(x) is called the integrand, x is called the integration variable and the “c” is called the constant of integration.

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