Definite Integral Problem... I think?

[Hippofrog]

This problem is really confusing, I have no idea what it means or what to do. An answer would be optimal, but an explanation is still good, as long as you understand that I am really not that talented at this stuff.

 

[mmm4444bot]

I have no idea what it means or what to do.

Please explain the very first thing that you do not understand. Do not reference outside commercial sites. Our posting guidelines may be found in the post titled "Read Beofre Posting".

 

[Hippofrog]

Please explain the very first thing that you do not understand. Do not reference outside commercial sites. Our posting guidelines may be found in the post titled "Read Beofre Posting".

Sorry, I didn't have any other way to post the problem without posting that website. Unfortunately, when I said I don't understand anything, I really meant it. I don't understand what the question is looking for, what 1/2m(m+1) means, and what the P=(n-1)b/n means.

 

[mmm4444bot]

I didn't have any other way to post the problem

What?! Have you not heard of cut-and-paste, editing, et cetera?

Results from Algebra II can sometimes be used to evaluate definite integrals. Recall that for each integer m:

1 + 2 + ... + (m − 1) + m = (1/2)(m)(m + 1)

Similar methods go back to Archimedes almost 2000 years before Newton invented calculus!

(i) Let f be the function defined on the interval [0, b] by

f(x) = 3x

and P = {0, b/n, 2b/n, ..., (n-1)b/n, b}

the partition subdividing [0, b] into n subintervals of equal length. Use the fact that

1 + 2 + ... + (m − 1) + m = (1/2)(m)(m + 1)

is true for all integers m to find the value of the Upper Sum Uf (P).

 

[mmm4444bot]

when I said I don't understand anything, I really meant it

You may need to pay a visit to your instructor's office hours, or drop calculus and review precalculus. (Or skip this exercise.)

 

[Hippofrog]

I understand Calculus, its just this one problem I do not understand. The way its worded and the ideas its trying to get across just don't make sense to me.

 

[mmm4444bot]

Please explain the very first thing that you do not understand.

How are your skills at paying attention?

 

[Hippofrog]

not good lol