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lecture31

# lecture31 - Lecture 31 1 Lecture 31(Sec 6.2 Integration by...

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Lecture 31 1 Lecture 31: (Sec. 6.2) Integration by Substitution, Part I ex. How can we evaluate integraldisplay 6 x (3 x 2 2) 5 dx ?

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Lecture 31 2 To see why we can use substitution: Let F be an antiderivative of a given function f . Then if g is a differentiable function of x , d dx [ F ( g ( x ))] =
Lecture 31 3 We have the following result: integraldisplay f ( u ) du dx dx =

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Lecture 31 4 Evaluate each integral: ex. integraldisplay (3 x 2 + 1)( x 3 + x 2) 15 dx ex. integraldisplay 5 x 4 3 radicalbig (4 x 5 ) 2 dx
Lecture 31 5 These are examples of the General Power Rule of Integration Let u be a differentiable function of x . Then integraldisplay u n du dx dx = NOTE:

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Lecture 31 6 But consider the following example: Evaluate integraldisplay 5 x radicalbig x 2 1 dx
Lecture 31 7

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lecture31 - Lecture 31 1 Lecture 31(Sec 6.2 Integration by...

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