This means that any two functions which differ by only a constant will have the same antiderivative Fundamental theorem of calculus Theorem 1 If f is a real-
We'll start out this semester talking about antiderivatives If the derivative of a function F isf, that is, F/ = f, then we say F is an antiderivative of f
Antiderivatives Definition 1 (Antiderivative) If F (x) = f(x) we call F an antideriv- ative of f Definition 2 (Indefinite Integral)
Proof This is a reformulation of the Constant Function Theorem from section 3 10 We also notice that if F(x) is an antiderivative of f(
antiderivatives 1 Derivatives Find the derivative of each of the following functions (wherever it is defined): 1 f(t) = t2 + t3 ? 1 t4 Answer: f (t) =
The Antiderivative maplet is an interface to the visual relationship between a function and its antiderivatives The Integration maplet is a calculator-like
These are the antiderivative formulas you should memorize for Math 3B Antiderivatives of more complicated functions can be computed from these using
Antiderivatives also have rules for these situations that are very similar to the derivative rules Constant Multiple Rule If you have a constant times a
A question remains: Are the functions F(x) = x2 + C (C any real number) all of the possible antiderivatives of f(x)=2x? Since the graph of any antiderivative
EXAMPLE 1 1 Finding Several Antiderivatives of a Given Function Find an antiderivative of f by computing derivatives of the proposed antiderivatives
We'll start out this semester talking about antiderivatives If the derivative of a function F isf, that is, F/ = f, then we say F is an antiderivative of f
22B Antiderivatives 2 Definition: Antiderivative We call F an antiderivative of f on the interval, I, if DxF(x)=f(x) on I ie If F'(x)=f(x) for all x on the interval
xx 2 3x Indefinite Integral The collection of all antiderivatives of a function is called the general antiderivative or indefinite integral of and denoted by Namely,