A=limn→∞Rn=limn→∞[f(x1)Δx+f(x2)Δx+...+f(xn)Δx](adsbygoogle = window.adsbygoogle || []).push({});

Consider the function f(x)=4√x, 1≤x≤16. Using the above definition, determine which of the following expressions represents the area under the graph of f as a limit.

I knew the correct answer was [tex]\sum \frac{15}{n} (4√x+\frac{15i}{n}) [/tex]

I figured out most of this, but the only thing I don't get is how you figure out is basically since you start the sum from i=1 to n, that you have to shift the sum up. If i=0, then I think there would be no "1+" term, right?

But let's say it was.... i =5 to n. I have no idea why, or where you would put the added terms in order for the sum to work. I thought that it would be outside of the function 4√x but inside of the summnation, because, well, you're just adding values, right?

I don't see or understand intuitively why 1+ would go inside of 4√x.

Similarly, I got this right but didn't understand the idea.

A=limn→∞Rn=limn→∞[f(x1)Δx+f(x2)Δx+...+f(xn)Δx]

Consider the function [tex]f(x) = \frac{ln(x)}{x}[/tex],3≤x≤10. Using the above definition, determine which of the following expressions represents the area under the graph of f as a limit.

Of course, the answer was Δx and [tex]\frac{ln 3+\frac{7i}{n}}{3+\frac{7i}{n}}[/tex], but just like above, wasn't sure why the [tex]\frac{ln3}{3}[/tex] went there. I thought if anything, it should be an added term, not mixed up with the main fraction.

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# Can someone explain this summation definition to me?

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