When finding derivatives there were rules for dealing with a constant times a function and the sum or difference of functions Antiderivatives also have rules
There are several derivative anti derivative rules that you should have pretty well-memorized at this point: It is very important that you know these well to
Section 4 9: Antiderivatives The following is a table of general antiderivatives that should be committed to memory: Basic Antiderivative Rules
There is a formula, called the Integration By Parts Formula, for reversing the effect of the Product Rule and there is a technique, called Substitution, for
The most general antiderivative of f (x) is then F(x) + C Original Function General Antiderivative 1 Constant Rule c (a constant) cx + C 2
If we have a definite integral, then we can either change back to xs at the end and evaluate as usual; alternatively, we can leave the anti-derivative in
Lesson 18 Antiderivatives and the rules for integration Many operations in mathematics have inverses For example, division is the inverse of
Given a function f(x), we say that F(x) is an antiderivative of f if F/(x) = f(x) We have the following rules for antiderivatives
Let us develop some rules for evaluating indefinite integrals (antiderivatives) The first will be the power rule for antiderivatives
fine to call them both C We should check that this is actually an antiderivative of f(x) We use the chain rule to get F
The most general antiderivative of f (x) is then F(x) + C Original Function General Antiderivative 1 Constant Rule c (a constant) cx + C 2
Antiderivative Introduction Indefinite integral Integral rules Initial value problem Table of Contents ◁◁ ▷▷ ◁ ▷ Page 1 of 15 Back Print Version
fine to call them both C We should check that this is actually an antiderivative of f (x) We use the chain rule to get F
By using known formulas and rules, you can easily find the derivative of almost any function 17 8 Theorem (Sum rule for antiderivatives) If f and g are functions
is any constant, is the set of all antiderivatives of f (x) = cos x antiderivatives of a function f , F(x) + C, is called the indefinite Ex Power rule of integration