Antiderivatives 5.1

Discovery of Power Rule for Antiderivatives If f ‘ (x) = Then f(x) = If f ‘ (x) = Then f(x) = If f ‘ (x) = Then f(x) = If f ‘ (x) = Then f(x) =

Tells us the variable of integration Differentiation Integration The process of finding a derivative The process of finding the antiderivative Tells us the variable of integration Symbols: Integral Symbols: Integrand

The antiderivatives vary by a constant! is the indefinite integral of f(x) with respect to x. Each function has more than one antiderivative (actually infinitely many) Derivative of: The antiderivatives vary by a constant!

General Solution for an Indefinite Integral You will lose points if you forget dx or + C!!! Where c is a constant

Basic Integration Formulas

You can always check your answer by differentiating! Find: You can always check your answer by differentiating!

Basic Integration Rules

C represents any constant Evaluate: C represents any constant

Evaluate:

Evaluate:

Evaluate:

Evaluate:

Particular Solutions and F(1) = 0