Notes_Exercises_Set04

# Notes_Exercises_Set04 - I 1 2 ANTIDERIVATIVES 0dx = c 1dx =...

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I. ANTIDERIVATIVES 1. c is called CONSTANT OF INTEGRATION 2. 3. k is a constant 4. POWER RULE 5. Antiderivative of reciprocal function is ln|x| function. 6. and Antiderivative of exponential functions Trigonometric functions 7. 8. Antiderivatives of Sum (or Difference) 9. Coefficient Rule Exercises 1: 1. + - + - + + - + dx x x x x x x x x x ) tan sec 4 2 4 3 7 3 5 sin 3 4 ( 5 3 4 2 - - dx x x x ) 1 4 ( 3 3 3. + - dx x x x x ) 5 cos cot tan cos 4 ( 2 2 4. - - - dx x x x x 3 3 5 2 2 2 c dx = 0 c kx kdx + = 1 , 1 1 - + + = + n c n x dx x n n c x dx x dx x + = = - ln 1 1 c a a dx a x x + = ) ln( c e dx e x x + = c x dx x + = ) sin( ) cos( c x dx x + - = ) cos( ) sin( c x dx x + = ) tan( ) ( sec 2 c x dx x + - = ) cot( ) ( csc 2 c x dx x x + = ) sec( ) tan( ) sec( c x dx x x + - = ) csc( ) cot( ) csc( ± = ± dx x g dx x f dx x g x f ) ( ) ( ) ( ) ( = dx x f k dx x kf ) ( ) ( c x dx dx + = = 1

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II. ABSORBER-TYPE SUBSTITUTION METHOD (ASM) This method is a reverse process to the CHAIN RULE – based differentiation. Note that:
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Notes_Exercises_Set04 - I 1 2 ANTIDERIVATIVES 0dx = c 1dx =...

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