I need some help with the following problem:

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> Find the torque around the x axis of the triangle with vertices (0, 0), (1, 4) and (1, 0). Assume the density equals one. — *Life of Fred Calculus*, Stanley F. Schmidt
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To be perfectly clear, this is the entire problem: there is no weight or force given!

Here are my thoughts on the problem / what I have already tried.

1. The triangle is essentially the graph $f(x) = 4x$ on $[0, 1]$
2. Elsewhere in the book, the author makes the assumption that weight is equal to $density \times x$, so $\tau = weight \times arm = 1 \times x \times arm$
3. It seems to me that the y-values of the points on the hypotenuse of the triangle (the values of $f(x)$) represent the arm length of torque. Thus,$$\int\_0^1 4x\, dx = 2x^2 \Big]\_0^1 = 2$$

$2$, therefore, is what I believe the answer to the problem *should be*. The answer book says that the answer is $\frac{8}{3}$. I have checked the author's errata page for the book, and this problem isn't listed. How do I solve this problem?