Lecture10bc - The function which is to be dv by whichever...

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Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009 Welcome to Math 122 Lecture 10 Survey of Calculus and its Applications I1 ! Integration by Substitution If u = g ( x ), then
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§ 9.2 Integration by Parts ! Integration by Parts ! Using Integration by Parts
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G ( x ) is an antiderivative of g ( x ). We can also write this as ! When u-substitution does not work ! When there is a mix of two types of functions such as an exponential and polynomial, polynomial and log, etc. ! When all else fails.
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Choose which of two functions is to be u? L: Logarithmic functions I: inverse trigonometric functions A: : Algebraic functions T: trigonometric functions E: Exponential functions.
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Unformatted text preview: The function which is to be dv by whichever function comes last in the list since functions lower on the list have easier antiderivatives Evaluate. Our calculations can be set up as follows: u = f x ( ) = x " f x ( ) = v = G x ( ) = Then x 2 x " 3 ( ) 3 # dx = Differentiate Integrate Evaluate Our calculations can be set up as follows: Then x 2 e x " dx = Notice that the resultant integral cannot yet be solved using conventional methods. Therefore, we will attempt to use integration by parts again . Our calculations can be set up as follows: Then 2 x " e x # dx = Therefore, we have x 2 e x " dx = Evaluate ln x " dx Evaluate ln x x 5 " dx...
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Lecture10bc - The function which is to be dv by whichever...

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