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The Fundamental Theorems of Calculus
Lesson 5.4
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First Fundamental Theorem of Calculus
Given f is continuous on interval [a, b] F is any function that satisfies F’(x) = f(x) Then
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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
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Area Under a Curve Consider Area =
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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]")
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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
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Second Fundamental Theorem of Calculus
Suppose we are given G(x) What is G’(x)?
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Second Fundamental Theorem of Calculus
Note that Then What about ? Since this is a constant …
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Second Fundamental Theorem of Calculus
Try this
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Assignment Lesson 5.4 Page 329 Exercises 1 – 49 odd
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