Which of the following is NOT true for all possible non-zero choices of integers m, n; m ≠ n, or all possible non-zero choices of real numbers p, q; p ≠ q, as applicable?

Options :

1. $\frac{1}{\pi }\underset{0}{\overset{\pi }{\int }}\sin m\theta \sin n\theta d\theta =0$

2. $\frac{1}{2\pi }\underset{-\pi /2}{\overset{\pi /2}{\int }}\sin p\theta \sin q\theta d\theta =0$

3. $\frac{1}{2\pi }\underset{-\pi }{\overset{\pi }{\int }}\sin p\theta \cos q\theta d\theta =0$

4. $\underset{\alpha \to \mathrm{\infty }}{lim}\frac{1}{2\alpha }\underset{-\alpha }{\overset{\alpha }{\int }}\sin p\theta \sin q\theta d\theta =0$