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If $f (x) = A \sin \frac{π x}{2} + B, f^{'} (1 / 2) = \sqrt{2}$ and
$\int_{0}^{1} f (x) d x = \frac{2 A}{π}$ then the constants $A$ and $B$ are respectively

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π/2,π/2

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detailed solution

Correct option is D

f′(x)=Aπ2cos⁡π2x⇒2=f′12=Aπ22so A=4π Also 2Aπ=∫01 f(x)dx=−A2πcos⁡π2x+Bx01=B+2Aπ ⇒ B=0

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If f(x)=Asin⁡πx2+B,f′(1/2)=2 and∫01 f(x)dx=2Aπthen the constants A and B are respectively

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free study material

If $f (x) = A \sin \frac{π x}{2} + B, f^{'} (1 / 2) = \sqrt{2}$ and
$\int_{0}^{1} f (x) d x = \frac{2 A}{π}$ then the constants $A$ and $B$ are respectively