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In this interesting essay explaining the performance gap among minorities in elite universities, there is an anecdote at the very bottom of the essay which intrigued me. Here's the screenshot:

Gather; Don't Strew, by Bob Weinstock

I feel left out of the joke. Can anyone explain what's going on here?

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up vote 13 down vote accepted

It is similar to:

Question:) How much is $500 \times 10^3$?

Answer1:) $500 \times 10^3 = 500 \times (9+1)^3 = 5(9^3 + 3\times 9^2 + 3\times 9 + 1) \dots = $

Answer2:) It is $500 \times 1000 = 1000 + 1000 + \dots = $

The point is the integral can be evaluated easily as

$\int_{0}^{1} (1-x)^3 \text{ d}x = -(1-x)^4/4 |_0^1 = -(1-1)^4/4 + (1-0)^4/4 = 1/4$

The joke is that most students did it the hard way by expanding $(1-x)^3$, while one student, computed the anti-derivative easily (giving some hope to the teacher), but then made it even harder by trying to expand that instead of just plugging in the values...

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Ah! Now I see it, thanks! – Duopixel Sep 1 '11 at 13:47

The joke is that although the student integrated the function using substitution to get $\frac{(1-x)^4}{4}$ instead of substituting the limits of integration directly into this compact form he multiplied it out and made significantly more work for himself.

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