Download presentation
Presentation is loading. Please wait.
1
Integration
2
The Reverse of the Derivative is the Antiderivative
Also called the Integral (symbol ∫ ) Why would you need it? - If you knew velocity (s’) but wanted to get position (s) - If you know the growth rate (p’) and want to get the population (p)
3
Definition A function (F) is called an antiderivative of f if F’(x) = f(x) for all x on an interval Example: f(x) = x2 F(x) =
4
From the previous example, we notice that F(x) = x2 could have many antidervivatives that work
5
General Form If F is an antiderivative of f, then the most general form of the antiderivative is F(x) + C where C is a constant
6
Common Antiderivatives
7
Example
Similar presentations
![If f (x) is a differentiable function over [ a, b ], then at some point between a and b : Mean Value Theorem for Derivatives.](/15/4748663/big_thumb.jpg "If f (x) is a differentiable function over [ a, b ], then at some point between a and b : Mean Value Theorem for Derivatives.>")
![The Fundamental Theorems of Calculus Lesson 5.4. First Fundamental Theorem of Calculus Given f is continuous on interval [a, b] F is any function.](/33/8262640/big_thumb.jpg "The Fundamental Theorems of Calculus Lesson 5.4. First Fundamental Theorem of Calculus Given f is continuous on interval [a, b] F is any function.>")
