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

2. First, a little review: Consider: then: or 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:findWe 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

15. Front Cover #15?

16. 4.1 Antiderivatives and Indefinite Integration

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, 15-47 odd,55-63 odd 73,77, 79 Thurs: MMM pg. 124-125 Fri: More practice problems (4.1)