If \(f(x) = R \: \sin ( \frac{\pi x}{2}) + S, f’\left(\frac{1}{2}\right) =…

GATE · 2017 · CS · Set 2 · Computer Science & IT

If f(x)=R sin⁡(πx2)+S,f’(12)=2f(x) = R \: \sin ( \frac{\pi x}{2}) + S, f’\left(\frac{1}{2}\right) = \sqrt{2} and ∫01f(x)dx=2Rπ\int_0^1 f(x) dx = \frac{2R}{\pi}, then the constants RR and SS are

  1. A.

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

  2. B.

    2π\frac {2} {\pi} and 00

  3. C.

    4π\frac {4} {\pi} and 00

  4. D.

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

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