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14209an6.1-3 - c Kendra Kilmer April 2 2009 Section 6.1...

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c Kendra Kilmer April 2, 2009 Section 6.1 - Antiderivatives and Indefinite Integrals Example 1: What are the possible functions whose derivative is x ? Definition: The General Antiderivative of f ( x ) on an interval is F ( x ) + C , where C is any real number constant, if Also written as which is known as the indefinite integral of f , where F 0 ( x ) = f ( x ) Note: Antidifferentiation (or integration) is the inverse operation of . Rules of Integration: 1. Z x n dx = 2. Z k dx = 3. Z e x dx = 4. Z 1 x dx = 5. Z [ f ( x ) ± g ( x )] dx = 6. Z [ k · f ( x )] dx = 1
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c Kendra Kilmer April 2, 2009 Example 2: Find the following: a) Z 8 dx b) Z x 5 dx c) Z 1 3 x 4 dx d) Z 2 t 9 dt e) Z ( 5 x 4 + x 3 - 2 ) dx f) Z 3 x dx g) Z ( e x + x 3 ) dx h) Z ( 3 x - 1 x 2 - x 3 2 ) dx i) Z 4 x 2 + x 3 8 x dx j) Z ( x - 2 )( x + 3 ) dx 2
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c Kendra Kilmer April 2, 2009 Example 3: Find y if y ( 1 ) = 1 and
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