Let $$g_{i} : \left[\frac{\pi}{8},\frac{3\pi}{8}\right] \rightarrow R, i = 1,2$$, and $$f:\left[\frac{\pi}{8},\frac{3\pi}{8}\right] \rightarrow R$$ be function such that
$$g_{1}(x) = 1, g_{2}(x) = |4x-\pi|$$ and $$f(x) = \sin^{2} x$$, for all $$x \epsilon \left[\frac{\pi}{8},\frac{3\pi}{8}\right]$$
Define
$$S_{i} = \int_{\frac{\pi}{8}}^{\frac{3\pi}{8}} f(x)\cdot g_{i}(x) dx, i- 1, 2$$