JEE Advanced 2021 · Paper 2, Mathematics question 11

Question Stem for Question Nos. 11 and 12

Let $g_i: \left[\frac\pi8, \frac{3\pi}8\right] \to \mathbb R$, $i = 1, 2$, and $f: \left[\frac\pi8, \frac{3\pi}8\right] \to \mathbb R$ be functions such that
$$g_1(x) = 1,\quad g_2(x) = |4x - \pi| \quad\text{and}\quad f(x) = \sin^2 x,\quad\text{for all } x \in \left[\frac\pi8, \frac{3\pi}8\right]$$
Define
$$S_i = \int_{\pi/8}^{3\pi/8} f(x)\cdot g_i(x)\,dx,\qquad i = 1, 2$$