T minus 40 and suddenly the words are red before me. I don’t recall the substitution for i-cubed and no matter what I do, I have to get this problem right: It’s worth six points, a guaranteed B if I miss it.

I take a breath and flip over one of my scraps of paper and start writing:

cn=n

i=(n^{2}+n)/2

i^{2}=(2n^{3}+3n^{2}+n)/6

i^{3}=(n^{4}+ +n)/4

And here I freeze. I’m missing a term. I remember looking over the substitutions in my notes last night–God, why didn’t I take care to remember i-cubed?–and recall thinking, It’s a test. He can’t possibly do i-cubed, can he?

I close my eyes and try to recreate the page before me. Tentatively, I scribble in “3n^{2}” and hold my breath.

It *looks* right, so I breathe a sigh of relief and continue.

I stop before I even start. The first term of my problem is i^{3}/n^{3}. If I try to substitute in (n^{4}+3n^{2}+n)/4, I’ll end up with n/4–and that’ll give me an infinite answer! And since the area bounded by x^{2}=1, x=0, x=1, and the x-axis is most certainly *not* an infinite area, I’ve got it wrong *again*.

I take another deep breath and look over my work so far. I copied the function correctly. Delta-x is correct, too: (b-a)/n –> (1-0)/n = 1/n. Even M_{i} is correct! (a+i(delta-x) –> 0+i(1/n) = i/n)

So *what* am I doing wrong? *Where* have I made a mistake?

I keep looking. I have to go over everything twice before–BAM!–I suddenly realise what I did wrong: I substituted M_{i} instead of delta-x, and since i/n definitely does *not* equal 1/n, there–at last–is my error.

So I erase a couple terms and then rewrite them and finally end up with i-squared, whose substitution I easily recall, and within minutes, I’m done. (:

Now to await the results. And it’s T minus two days for that.

Your brain confuses and terrifies me- but in the good way.

Tell us your grade when you get it, even if I’m pretty sure it’ll make me envious!

Nick! <3

I do hope you're doing well, by the way. I miss you. :(

In any case, although I don't know my exact grade for the final, my final grade for the class was an A. :)