For each function $f(x)$, say which of the choices are anti-derivatives $F(x)$.
[Start with some simple algebraic forms]
* $f(x) = x$
1. $F(x) = 2 x + 3.5$
2. $F(x) = 2 x^2 - 1$
3. $F(x) = \frac{1}{2} x^2 + 5$
4. $F(x) = \frac{1}{2} x$
[Then move to forms where the student needs to differentiate the choices and compare them to the original function.]
* $f(x) = e^{-k x} \sin(\frac{2 \pi}{P} x)$
1. $F(x) = - \frac{P e^{-kx}\left(k P \sin(\frac{2\pi}{P}x) + 2 \pi \cos(\frac{2 \pi}{P}x) \right)}{k^2 P^2 + 4 \pi^2}$
2. And some others that aren't right.