5_4 - Section 5.4: Indefinite Integrals and the Net Change...

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Unformatted text preview: Section 5.4: Indefinite Integrals and the Net Change Theorem Instructor: Ms. Hoa Nguyen (nguyen@scs.fsu.edu) Reminder about the Fundamental Theorem of Calculus 1. If g ( x ) = R x a f ( t ) dt , then g ( x ) = d dx R x a f ( t ) dt = f ( x ). 2. R b a f ( x ) dx = F ( b )- F ( a ) where F is any antiderivative of f , i.e., F = f or F = R f ( x ) dx (indefinite integral). The difference between indefinite and definite integrals A definite integral R b a f ( x ) dx is a number . An indefinite integral R f ( x ) dx is a function (or family of functions). The second part of the Fundamental Theorem of Calculus shows the connection between these two integrals: Z b a f ( x ) dx = F ( b )- F ( a ) = F ( x )] b a = Z f ( x ) dx ] b a Table of Indefinite Integrals (check the hand-out) Example 1 of Section 5.4 (textbook): Example 2 of Section 5.4 (textbook): Example 3 of Section 5.4 (textbook): Example 4 of Section 5.4 (textbook): Example 5 of Section 5.4 (textbook): Applications The Net Change Theorem...
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