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Thread: Find a closed form expression for the nth right Riemann sum of this integral.

  1. #1

    Find a closed form expression for the nth right Riemann sum of this integral.

    Consider the following definite integral:

    . . . . .[tex]\displaystyle \int_6^{11}\, (-5x\, +\, 1)\, dx[/tex]

    Find a closed-form expression for the nth right Riemann sum of this integral.



    How do you figure these kind of questions out?
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    Last edited by stapel; 12-08-2017 at 12:24 PM. Reason: Typing out the text in the graphic.

  2. #2
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    Quote Originally Posted by DeezNuts View Post
    Consider the following definite integral:

    . . . . .[tex]\displaystyle \int_6^{11}\, (-5x\, +\, 1)\, dx[/tex]

    Find a closed-form expression for the nth right Riemann sum of this integral.



    How do you figure these kind of questions out?
    You need to remember and then apply to your SPECIFIC problem the GENERAL definition of a right Riemann sum, namely

    Expressed in function notation it is: [tex]\displaystyle \sum_{j=1}^n \,\Bigg[\,\bigg\{f\left ( a\, +\, j\, \cdot\, \dfrac{b\, -\, a}{n} \right )\bigg\}\, \cdot\, \bigg\{ \dfrac{b\, -\, a}{n}\bigg\}\,\Bigg][/tex]

    In your specific problem, what is the value of a?

    The value of b?

    And what is f?

    What will be the argument of f (the part inside the parentheses after the f) when j = n?
    Last edited by stapel; 12-08-2017 at 12:29 PM. Reason: Copying typed-out graphical content into reply.

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