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MIT student blogger Sam M. '07

Underneath your curves by Sam M. '07

(Free) sample problems from MIT's integration bee this year.

DID YOU KNOW? The new wave-y pop song “I Should Be Allowed To Think” by They Might Be Giants begins with the lyrics, “I saw the best minds of my generation destroyed by madness, starving, hysterical…”

Hello readers.

I’ve had an overwhelming number of requests for sample problems from this year’s integration bee at MIT.

But first, a little bit about my life.

Last night I made my TV boyfriend Alton Brown’s recipe for 40 Cloves and a Chicken. Basically you sear the chicken, cover it in oil, toss in 40 cloves of garlic, which incidentally take a surprisingly long time to peel, and forget about it in a 350 degree oven for 90 minutes. As Alton suggests in his “In the Bulb of the Night” episode, the leftover oil indeed makes arguably the best garlic bread in the entire world.

After that, I headed over to the floor lounge to play Super Mario Kart with Gabe. Three hours later, I realized that maybe bringing my Super Nintendo back to MIT for IAP was not the best idea that I have ever had in my short but colorful life.

That is all.

So, here’s some sample problems that I meant to put up with my entry the MIT Integration Bee last week.


Each one should take you no more than four minutes to solve. Constants of integration are not necessary. No knowledge beyond one year of single-variable calculus should be necessary.

Work hard! This took me like eleven minutes to make for you in Paint. Yes, dear, I do know how to use Mathematica, but I’m in lab right now and I don’t have it on this computer, so I figured this would be way, way easier.

No, not the girl who builds robots.

And while I’m thinking of it, that brings us to…


If you were describing an integral in words to somebody and you had to say, out loud, the symbol “ln x,” how would you pronounce it?

1. “Natural log of x”
2. “Natural log x”
3. “Lynn x” (rhymes with “win”)
4. “Lonn x” (rhymes with “gone”)
5. “Log x”
6. other (please specify)

Coming attraction: Sweet suite painting.

36 responses to “Underneath your curves”

  1. chian-chisa says:

    6 like Kevin Wallace I’d say l n x , though if it makes the person more confused I’d say 5 log x instead.

  2. Helen says:

    So after looking at those, I’m beginning to think that my calc teacher is correct in giving me a B+ (for not doing journals raarh).

    Hmm… I don’t think I Should Be Allowed To Think is new (I’ve been listening to it for like… 3+ years now, and a quick search shows that it was released in 1994), but that’s certainly interesting. :O

  3. Ruth says:

    I would also say “L N of X”.

    I watched Alton Brown yesterday (recognized by the link to his blog from here) and he’s awesome. He explained how to cook an artichoke, put my intimidation at the multi-facted plant to rest, and gave a brief history of the various uses for all parts of the plant. The only part that sucked was finding out how little of the leaves are edible. How ungratifying.

    Then I watched Project Runway. Santino #1.

  4. Sam Hardy says:

    Ye haven’t got a chance boy! Integrate, Bobert Integrate!(Bad Forrest Gump reference)

  5. Anonymous says:

    Should I post them?

  6. Robb Carr says:

    Err that was me sorry,

  7. Mike Axiak says:


    I couldn’t help but mention you can use LaTeX to generate the images in nicer quality tongue laugh

    If anyone would like to generate nice images without installing LaTeX, I wrote a thing on my website to do it for you:

    For anyone curious, the text I typed in for the above integrals is:

    int{sqrt{frac{x}{1-x^3}}, dx} \\

    int{e^{arccos{x}}, dx} \\

    int_0^{pi}{cos{7x}cos{17x}cos{37x}, dx} \\

    int{sin{101x}sin^{99}{x}, dx} \\

    int{frac{1}{ln{x}} + ln{(ln{x})}, dx} \\

    int_0^{frac{pi}{2}}{ln{(sin{x})}, dx}

    Okay, shared enough geekiness for this hour wink.

  8. Sam says:

    Heh, thanks Mike. I’m still pretty proud of my hand-drawn integral swooshes (you would think an MIT student would have a better name for those), but I’ll totally use your LaTeX thing the next time I need to post an integral on the blog.

  9. 6. Other!

    I would just say “ell enn ex”. If l or n were variables in the problem, I would probably revert to “Natural log of x”. I haven’t encountered this, but I haven’t done much multi-variable calculus yet.

  10. Teck Lee says:

    When I was first taught it in Singapore, everyone said “lonn x”. Then I moved to Florida, USA, and everyone here says “ell enn of x” so I’ve become used to that.

    So my vote would be “ell enn of x” or any equivalent alternative.

  11. Kate says:

    Either “lynne x” or “natural log of x” — depends whether I’m rushing or not.

    Alton Brown is the man, by the way. :D

  12. dally says:

    “ell en ex”

  13. Mike Axiak says:

    Yea, for hand-drawn those are really good.

    You should’ve seen integral swooshes before Knuth made TeX! Reading the AMM before 1980 is fun for that very reason…(you can almost sense the desperation emanating from Knuth)

  14. Mike Axiak says:

    Funny how there’s an *interesting* debate about the pronounciation of ‘ln’…I call it log.

    ln x = log of x

    log_10 (x) = log base 10 of x or ‘common’ log of 10

    Most advanced math books I’ve read don’t even mention log base 10…lg (log base 2) is much more common.

  15. Laura says:

    Ahh integrals. Bleh.

    As for “ln x,” I’d probably say “natural log of x,” but in context (like you’re doing math problems and rattling off a long term or something), I’d probably just shorten it to “ln x.” As in the letters l,n, and x. Just the way it looks.

  16. Mike says:

    That They Might Be Giants song is indeed interesting. And your Allison impression is remarkable.

    As for the poll, I prefer 3: lynn x, but I’m just a poor ignorant soul who chose to go to a liberal arts college.

  17. Anonymous says:

    I would say “natural log of x”. On another note yall should definitely check out this video. It’s hilarious.—The-Chronic-of-Narnia-Rap?v=zLElfJ9YCh0&feature=Favorites&page=1&t=t&f=b


  18. jpl says:

    oh man, i did all of them except the sin[101x] integral. damn it took me so long. were you given formulas like the addition/subtraction formulas for sin or cos? I should probably have those memorized, but oh well…god i feel so stupid

  19. Anonymous says:

    I want to add my vote under the (6) category for Alan x/ ell enn x/ L.N. x, etc.

    I thought i was going to be original in this response… i guess its too late for that.

    oh well raspberry

  20. Kelley says:

    Wow. I am most definitely a 1) natural log of x person. I guess I’m just obsessive like that. By the way, thanks for putting up some sample Integration Bee Questions!

  21. Mike says:

    ell enn x/ell enn of x

  22. Scott says:

    Ell enn ex for sure. I often find myself speaking in TI calculator shorthand language. Sometimes I’ll explain a calculation pronouncing “second ans” for the previous answer or “stat edit” to get to the list editor, for example. Easier to translate into button presses if you say exactly what you see. smile

  23. Jina says:

    Funny, I had a discussion about this very topic in math class on this very today right before reading your blog on said topic. How extremely coincidental and weird. Anyhow, here’s how our class voted:

    1/2 of the class: “lonn x”

    other 1/2 of the class: “lynn x” (but they spelled it “linn x”)

    teacher: “It’s ‘natural log of x’ you morons, stop being lazy!”

    me: “Are you allowed to say line x”? Yeah for being unique!

    Anyhow, my vote is for number 6, other, or more specifically, “line x”

  24. Jared says:

    I’m actually a lynn x type of person. I infuriated my calc teacher because he was a stickler for the ‘natural log of…’ stuff.

    Awesome entry, I’ll try those integrals later.


  25. uren says:

    2. Natural Log x. (at least thats how we pronounce it in our school;)

    btw… i’ve heard many good universities give out likely letters to top prospective “admitted” UG students well b4 April 1. Is MIT one of them?

  26. Maria says:

    natural log of x. i was actually having this debate yesterday with a friend in physics class, so i just had to reply. she liked calling it log natural x.

  27. Sam says:

    Answers to comments, while my reactor heats up.

    Robb “Anonymous” Carr — I’ll post the answers this week sometime when I get around to using the Integrator (I didn’t write down the answers from the bee).

    Ruth — Urgh… Artichoke… a dissection food. I guess it’s okay, but I’ve never been the biggest fan in the world. What do you mean by Santino #1? What episode could you possibly have watched that you ended up with a positive impression of Santino?

    JPL — No, we weren’t given the addition/subtraction formulas, and believe me, those are one of those things that you encounter in the middle of a pset and you’re like, “Oh dear, they want me to do THAT?” Like solving a differential equation or doing a laplace transform or something.

    Uren — I heard from MIT around the third week of March… sometime between the 15th and the 22nd, I think.

  28. dinyar says:

    hi, great entry and i’d also go for 6. “ell en x”

  29. Kelley says:

    My calc teacher frequently just calls it the log. This can make it interesting when she actually is talking about a logarithm in base 10. My favorite log comment is “If there are variables flying around in the air, just throw a log at them and they’ll fall down.”

  30. Alexandre says:

    1st column, third one down, how do you do it? I tried several variations of parts, but nothing’s happening for me. T-sub & partial fractions are definately out, and I don’t know what to set u equal to if it’s A-sub.