2.7 Class Notes

# 2.7 Class Notes - March 8 HWK#6 due R 3/15 or F 3/16 7.1 10...

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March 8 HWK #6 due R 3/15 or F 3/16 7.1: 10, 16, 24, 33, 36, 39 7.2: 10, 14, 18, 24, 32, 34 Spring Break March 17-25 Prelim 2: Thursday March 29 Covers up to and including 7.2. Integration If F (x) = f(x) then F is an antiderivative of f. Fact. If F and G are antiderivatives of f then F-G is a constant . If f(t) is velocity at time t, then F(t) is position. From velocity we can only determine position up to a constant F(0). Indefinite integral If '( ) ( ) then we write ( ) ( ) F x f x f x dx F x C = = + We say F is the indefinite integral of f. This is just another word for antiderivative. +C reminds us that one we have one antiderivative we get all the others by adding a constant. Integration Formula 1 1 1 ( 1) when 1 1 I1. 1 1 p p p p p d x p x x p x x dx C p dx p p + + + = = + = + + + Problem 1 5 2 3 Find the antideriv ative of 2 6 7 1 1 p p x x dx C x x x p x p + = + ≠ − + + + + Solution 5 2 5 2 1/2 3 3 6 3 3/2 2 1 Find the antiderivative of 2 I don't wri 1 1 te th 6 7 6 7 2 7 2 3 3 e +C p p x x x x x x x x x x x dx C x x p p x + + + + = + + + + + = + +

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