#order-of-integration

Question 1: Single choice

For $f(x, y) = \frac{xy(x^2 - y^2)}{(x^2 + y^2)^3}$ on $[0, 2] \times [0, 1]$ , the iterated integrals are $\int_0^2\int_0^1 f\,dy\,dx = 0.2$ and $\int_0^1\int_0^2 f\,dx\,dy = -0.05$ . Why can the order of integration change the result?

$\iint |f|$ is infinite near the origin, so Fubini's theorem does not apply1
One computation must be wrong, since the order never matters for a rational function2
The region is not a square, and Fubini's theorem needs equal side lengths3
$f$ changes sign on the region, and Fubini's theorem requires $f \ge 0$ 4

#order-of-integration

Timed test