Integration - Integration and Its applications MAT 1300 C Winter 2014 1 ANTIDERIVATIVES AND INDEFINITE INTEGRALS 1 2 Antiderivatives and Indenite

# Integration - Integration and Its applications MAT 1300 C...

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Integration and Its applications MAT 1300 C Winter 2014
2 COMMON INDEFINITE INTEGRALS 3 2 Common Indefinite Integrals 1. For any constant k , Z k dx = kx + C. 2. For any real number n except -1, Z x n dx = 1 n + 1 x n +1 + C. 3. Z 1 x dx = ln | x | + C. 4. Z e x dx = e x + C. 3 Rules for Integrals 1. For any constant k and function f ( x ), Z kf ( x ) dx = k Z f ( x ) dx. 2. For any functions f ( x ) and g ( x ), Z f ( x ) + g ( x ) dx = Z f ( x ) dx + Z g ( x ) dx.
3 RULES FOR INTEGRALS 4 Ex: Find each of the following indefinite integrals.a)Rx2-5x+ 17dxb)R5ex-3x-2+ 7x-1dx
3 RULES FOR INTEGRALS 5 Don’t forget to simplify first if possible! Ex: Find each of the following indefinite integrals. a) R x (4 x - 3) 2 dx b) R e x +3 - 7 5 x dx
3 RULES FOR INTEGRALS 6 c) R 3 x + 5 e x - 7 x 2 dx d) R 2 x dx
4 INITIAL VALUE PROBLEMS 7 4 Initial Value Problems