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?

• A. \(\frac{1}{\pi }\mathop \smallint \limits_0^\pi \sin m\theta \sin n\theta d\theta = 0\)
• B. \(\frac{1}{{2\pi }}\mathop \smallint \limits_{ - \pi /2}^{\pi /2} \sin p\theta \sin q\theta d\theta = 0\)
• C. \(\frac{1}{{2\pi }}\mathop \smallint \limits_{ - \pi }^\pi \sin p\theta \cos q\theta d\theta = 0\)
• D. \(\mathop {\lim }\limits_{\alpha \to \infty } \frac{1}{{2\alpha }}\mathop \smallint \limits_{ - \alpha }^\alpha \sin p\theta \sin q\theta d\theta = 0\)