Download presentation
Presentation is loading. Please wait.
1
The Fundamental Theorems of Calculus
Lesson 5.4
2
First Fundamental Theorem of Calculus
Given f is continuous on interval [a, b] F is any function that satisfies F’(x) = f(x) Then
3
First Fundamental Theorem of Calculus
The definite integral can be computed by finding an antiderivative F on interval [a,b] evaluating at limits a and b and subtracting Try
4
Area Under a Curve Consider Area =
5
Area Under a Curve Find the area under the following function on the interval [1, 4]
![Area Under a Curve Find the area under the following function on the interval [1, 4]](http://slideplayer.com./slide/14329611/89/images/5/Area+Under+a+Curve+Find+the+area+under+the+following+function+on+the+interval+%5B1%2C+4%5D.jpg "Area Under a Curve Find the area under the following function on the interval [1, 4]")
6
Second Fundamental Theorem of Calculus
Often useful to think of the following form We can consider this to be a function in terms of x View Geogebra Demo View QuickTime Movie
7
Second Fundamental Theorem of Calculus
Suppose we are given G(x) What is G’(x)?
8
Second Fundamental Theorem of Calculus
Note that Then What about ? Since this is a constant …
9
Second Fundamental Theorem of Calculus
Try this
10
Assignment Lesson 5.4 Page 329 Exercises 1 – 49 odd
Similar presentations
![4-4: The Fundamental Theorems Definition: If f is continuous on [ a,b ] and F is an antiderivative of f on [ a,b ], then: The Fundamental Theorem:](/25/8063742/big_thumb.jpg "4-4: The Fundamental Theorems Definition: If f is continuous on [ a,b ] and F is an antiderivative of f on [ a,b ], then: The Fundamental Theorem:>")
![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.>")
