31 - Improp_IntRev

31 - Improp_IntRev - Ex. ! x ! 3 x 2 ! 5 x + 4 dx...

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Improper Integrals Continued Compare 1 x 2 and 1 x as x gets close to zero. Consider 1 x 2 dx 0 1 ! and 1 x 0 1 ! dx . What’s happening as x approaches zero? Define 1 x 2 dx 0 1 ! = lim t " 0 + 1 x 2 dx t 1 ! Define 1 x dx 0 1 ! = lim t " 0 + 1 x dx t 1 !
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Ex. 1 x ! 2 ( ) 2 0 3 " dx
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Do. Evaluate the following. Why are they improper? 1. 1 1 ! x 2 0 1 " dx 2. 1 x ln x ( ) 2 1 2 2 ! dx 3.
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Remember integration techniques
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Unformatted text preview: Ex. ! x ! 3 x 2 ! 5 x + 4 dx " Ex. Find the coefficient on the sin z 3 ! " # $ % & term in the evaluated integral of z sin z 3 ! " # $ % & dz . Ex. x 4 2 x 2 + 3 ! dx Ex. cos 3 ! 3 x ( ) dx "...
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31 - Improp_IntRev - Ex. ! x ! 3 x 2 ! 5 x + 4 dx...

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