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Math Help - Inequalities & A Definite Integral

  1. #1
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    Inequalities & A Definite Integral

    I don't understand the first step of the following proof (I was given the first step and I completed it fine, but it is the first step that I do not understand).

    Inequalities & A Definite Integral-codecogseqn-4-.gif

    First step:

    Inequalities & A Definite Integral-codecogseqn-6-.gif

    The rest of the proof was straightforward. From the first step, this next part comes from the fact that the resulting integral from the first step is less than or equal to:

    Inequalities & A Definite Integral-codecogseqn-7-.gif
    Anyways, I just need help understanding why the first step is true. Thanks for any help!!!
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  2. #2
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    Re: Inequalities & A Definite Integral

    Quote Originally Posted by zachd77 View Post
    I don't understand the first step of the following proof (I was given the first step and I completed it fine, but it is the first step that I do not understand).
    Click image for larger version. 

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    First step:
    Click image for larger version. 

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    It is a theorem in the theory of integrals:

    If f is integrable on [a,b] then |f| is integrable on [a,b] and

    \left| {\int_a^b f } \right| \leqslant \int_a^b {\left| f \right|}~.

    Is that the question?
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  3. #3
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    Re: Inequalities & A Definite Integral

    Yep! That is what I am looking for; I have not seen that property of integrals before.

    Thanks for the help!
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