GATE 2017 CS (CS2) – Question 20
$f(x)=R\sin(\pi x/2)+S$, $f\prime(1/2)=\sqrt2$ and $\int_0^1 f(x)dx=2R/\pi$. Find R,S respectively.
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Correct answer: (C) $4/\pi,0$
Explanation
Integration gives $2R/\pi+S=2R/\pi$, so S=0. Differentiating gives $f\prime(x)=(R\pi/2)\cos(\pi x/2)$. At x=1/2 this is Rπ/(2√2)=√2, yielding R=4/π. Therefore C.