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Estimate the area under the graph of f(x) = 6/x from x = 1 to x = 7 using 6 approximating rectangles and right endpoints.

I keep getting 1 for delta x because (B-A)/N, and then I get values 1,3,6,10,15,21. Then I plug each of those into f(x), add them all together, but I'm not getting the correct answer. Could someone let me know what I'm doing wrong? Thanks!

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$\Delta x=1$ is correct. Then you need to multiply by $f(x)$ at some point in the interval to get the area of the rectangle. The third rectangle ranges from $x=3$ to $x=4$, so $f(x)$ ranges from $6/3=2$ to $6/4=1.5$. Certainly it should not be $6$.

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  • $\begingroup$ It must be the x values I'm getting wrong. I get the x values and plug each into f(x), then add them all together. $\endgroup$ – Shelby Dec 4 '14 at 23:14
  • $\begingroup$ The $x$ values are just $1,2,3,4,5,6,7$, where the rectangles range from one to the one above. Maybe you can explain where $21$ came from? $\endgroup$ – Ross Millikan Dec 4 '14 at 23:16
  • $\begingroup$ I honestly don't know. Thank you for your help $\endgroup$ – Shelby Dec 4 '14 at 23:28
  • $\begingroup$ @Shelby: You are, indeed, getting the $x$-values wrong. Note that it says "using...right endpoints." What they mean by that is that for the function value $f(x)$ on the interval $\bigl[A+k\Delta x,A+(k+1)\Delta x\bigr],$ you should "plug in" $x=A+(k+1)\Delta x.$ For example, on the interval $[5,6],$ you should plug in $6.$ $\endgroup$ – Cameron Buie Dec 4 '14 at 23:28
  • $\begingroup$ Is 6 correct for the area of the first rectangle? $\endgroup$ – Shelby Dec 4 '14 at 23:38

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