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

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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 () Fx fx fxd x Fx 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 dx p x xp x xd x C p dx p p + + + == + = + + + Problem 1 52 3 Find the antideriv ative of 2 67 1 1 p p x x C xx x p x p + ++ + + Solution 1 / 2 3 3 633 / 2 2 1 Find the antiderivative of 2 I don't wri 1 1 te th 2 72 3 3 e+C p p x x x x x x x C p p x + + =+++ +
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Problem 3 2 Find the antiderivative of 2 8 xx x x ⎛⎞ + ⎜⎟ ⎝⎠ Solution 3 7/2 1/2 22 3/2 5/2 2 8 82 8 2 Answer 8 2 53 x + + = =+ ⋅+ Integration Formula 2 1 1 I2. 1 ln | l | n d dx dx x x x == = Integration Formula 3 I3. rx rx rx rx e ed r r dx x d ee = = Problem
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This note was uploaded on 11/14/2007 for the course MATH 1106 taught by Professor Durrett during the Spring '07 term at Cornell University (Engineering School).

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

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