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4.1 : Anti-derivatives Greg Kelly, Hanford High School, Richland, Washington.

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Presentation on theme: "4.1 : Anti-derivatives Greg Kelly, Hanford High School, Richland, Washington."— Presentation transcript:

1 4.1 : Anti-derivatives Greg Kelly, Hanford High School, Richland, Washington

2 First, a little review: Consider: or then: It doesn’t matter whether the constant was 3 or -5, since when we take the derivative the constant disappears. However, when we try to reverse the operation: Given: find We don’t know what the constant is, so we put “C” in the answer to remind us that there might have been a constant.

3 If we have some more information we can find C.
Given: and when , find the equation for . This is called an initial value problem. We need the initial values to find the constant. An equation containing a derivative is called a differential equation. It becomes an initial value problem when you are given the initial condition and asked to find the original equation.

4 4.1 Antiderivatives and Indefinite Integration

5 4.1 Antiderivatives and Indefinite Integration

6 4.1 Antiderivatives and Indefinite Integration

7 4.1 Antiderivatives and Indefinite Integration

8 4.1 Antiderivatives and Indefinite Integration

9 4.1 Antiderivatives and Indefinite Integration

10 4.1 Antiderivatives and Indefinite Integration

11 4.1 Antiderivatives and Indefinite Integration

12 4.1 Antiderivatives and Indefinite Integration

13 4.1 Antiderivatives and Indefinite Integration

14 4.1 Antiderivatives and Indefinite Integration

15 4.1 Antiderivatives and Indefinite Integration
Front Cover #15?

16 4.1 Antiderivatives and Indefinite Integration

17 4.1 Antiderivatives and Indefinite Integration

18 4.1 Antiderivatives and Indefinite Integration

19 4.1 Antiderivatives and Indefinite Integration

20 4.1 Antiderivatives and Indefinite Integration

21 4.1 Antiderivatives and Indefinite Integration

22

23 Basic Integration Rules
These two equations allow you to obtain integration formulas directly from differentiation formulas, as shown in the following summary.

24 Basic Integration Rules
cont’d

25 4.1 Antiderivatives and Indefinite Integration

26 Practice Exercises Original Rewrite Integrate Simplify

27 4.1 Homework HW 4.1 Wed: pg. 255, 5-14 all, odd,55-63 odd 73,77, 79 Thurs: MMM pg Fri: More practice problems (4.1)

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