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Math Help - Improper Integrals

  1. #1
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    Improper Integrals

    Improper Integrals-36.8.png

    Can someone give me a hint for this one ?
    It's from Elementary Analysis by Ross.
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  2. #2
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    Re: Improper Integrals

    Quote Originally Posted by kasper90 View Post
    Click image for larger version. 

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    Can someone give me a hint for this one ?
    It's from Elementary Analysis by Ross.

    Look at theorems 33.4 & 33.5.

    You know that f(x)\le |f(x)|.
    Thanks from kasper90
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  3. #3
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    Re: Improper Integrals

    Okay, I tried it. I thought about this:

    1. Let h := |f| - f
    2. h is continuous on (a,b) (as |f| and f are)
    3. 0 <= h <= 2 |f| (as -f <= |f| )

    than use 36.6 ?
    than integral h exist
    than integral h - |f| exist (as |f| exist)
    and integral f exist
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