Lecture Slides 23 - Antiderivatives Instructor Yang(Louis Liu Ph.D Michiga State University Instructor Yang(Louis Liu Ph.D Antiderivatives Steps In

# Lecture Slides 23 - Antiderivatives Instructor Yang(Louis...

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Antiderivatives Instructor: Yang (Louis) Liu, Ph.D. Michiga State University March 16, 2013 Instructor: Yang (Louis) Liu, Ph.D. Antiderivatives
Steps In Solving Optimization Problems Definition A function F is called an antiderivative of f on an interval I if F ( x ) = f ( x ) for all x in I . Instructor: Yang (Louis) Liu, Ph.D. Antiderivatives
Steps In Solving Optimization Problems Definition A function F is called an antiderivative of f on an interval I if F ( x ) = f ( x ) for all x in I . Theorem If F is an antiderivative of f on an interval I , then the most general antiderivative of f on I is F ( x ) + C where C is an arbitrary constant. Instructor: Yang (Louis) Liu, Ph.D. Antiderivatives
Examples and TableExampleFind the most general antiderivative of each of the followingfunctions1f(x) = sinx2f(x) = 1/x3f(x) =xn,n=-1 Instructor: Yang (Louis) Liu, Ph.D. Antiderivatives