If f (x) = R \sin ⁡ (\frac{\pi x}{2}) + S,\:f^{′} (\frac{1}{2}) = \sqrt{2}\:and\:\int _{0}^{1}⁡f (x) dx = \frac{2R}{\pi }, then the constants R and S are, respectively.

\frac{2}{\pi }\:and\frac{16}{\pi }

\frac{4}{\pi }\:and\frac{16}{\pi }

GATE Computer Science (CS) 2017 Shift 2 Solved Paper

Question : 20 of 65

Marks: +1, -0

f (x) = R sin \;⁡ (\;{π\;x}/{2}) + S,\:f^{′} (\;{1}/{2}) = {√{2}}\:and\:∫ _{0}^{1}⁡f (x) dx = \;{2R}/{π\;}

, then the constants R and S are, respectively.

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