# Can someone explain this anecdote from Bob Weinstock?

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:

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

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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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