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quiz_3_project

# quiz_3_project - Project Math 1920 Fall 03 Integration...

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Project Math 1920 Fall 03 Integration by (or of) Inverses: Integration by parts using a substitution of inverse functions leads to a rule that frequently yields good results: 1 1 1 11 1 1 () , Integration by parts , yfx yf xxf y df y f x dx y dy df y dy dx dy dy y f ydy df y u y dv dy dy xf x f −− =  ==  = =  =−   ∫∫ This method is based on taking the most complicated portion of the integral, the function f ( x ), and simplifying it first by using its inverse 1 f y Example: For the integral of ln x , we proceed ( ( ] 1 ln ln 1 1 1 cos ln , ln ln and for ( ) cos we get cos , cos cos sin sin cos cos cos sin y y y yy y y yx y x xdx y dy dx dy yd eC xxxC fx x x y y dx y dy y d y y C e e e ee e = =

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quiz_3_project - Project Math 1920 Fall 03 Integration...

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