Ta có:
$\int\limits_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\sin2x\sin7xdx$
$=\int\limits_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\dfrac{\cos 5x-\cos 9x}{2}dx$
$=\left(\dfrac{\sin 5x}{10}-\dfrac{\sin9x}{18}\right)\left|\begin{array}{l}\dfrac{\pi}{2}\\\dfrac{-\pi}{2}\end{array}\right.=\dfrac{4}{45}$