GATE CS 2017 Set 1 — Question 30

If \(f(x) = R\sin\left(\dfrac{\pi x}{2}\right) + S\), \(f'\left(\dfrac{1}{2}\right) = \sqrt{2}\) and \(\displaystyle\int_{0}^{1} f(x)\,dx = \dfrac{2R}{\pi}\), then the constants \(R\) and \(S\) are respectively