For each function \( f(x) \), say which of the choices are anti-derivatives \( F(x) \).

[Start with some simple algebraic forms]

- \( f(x) = x \)
- \( F(x) = 2 x + 3.5 \)
- \( F(x) = 2 x^2 - 1 \)
- \( F(x) = \frac{1}{2} x^2 + 5 \)
- \( F(x) = \frac{1}{2} x \)

[Then move to forms where the student needs to differentiate the choices and compare them to the original function.]

- \( f(x) = e^{-k x} \sin(\frac{2 \pi}{P} x) \)
- \( F(x) = - \frac{P e^{-kx}\left(k P \sin(\frac{2\pi}{P}x) + 2 \pi \cos(\frac{2 \pi}{P}x) \right)}{k^2 P^2 + 4 \pi^2} \)
- And some others that aren't right.