Consider the following definite integral:
. . . . .[tex]\displaystyle \int_6^{11}\, (-5x\, +\, 1)\, dx[/tex]
Find a closed-form expression for the n^{th} right Riemann sum of this integral.
How do you figure these kind of questions out?
Consider the following definite integral:
. . . . .[tex]\displaystyle \int_6^{11}\, (-5x\, +\, 1)\, dx[/tex]
Find a closed-form expression for the n^{th} right Riemann sum of this integral.
How do you figure these kind of questions out?
Last edited by stapel; 12-08-2017 at 12:24 PM. Reason: Typing out the text in the graphic.
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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