If \[f(x)=A\sin \left( \frac{\pi x}{2} \right)+B,\] \[{f}'\left( \frac – McqOptions

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1.	If \[f(x)=A\sin \left( \frac{\pi x}{2} \right)+B,\] \[{f}'\left( \frac{1}{2} \right)=\sqrt{2}\] and \[\int_{0}^{1}{f(x)\,dx=\frac{2A}{\pi },}\] then the constants \[A\] and \[B\] are respectively [IIT 1995]
A.	\[\frac{\pi }{2}\] and \[\frac{\pi }{2}\]
B.	\[\frac{2}{\pi }\] and \[\frac{3}{\pi }\]
C.	\[\frac{4}{\pi }\] and 0
D.	0 and \[-\frac{4}{\pi }\]
Answer» D. 0 and \[-\frac{4}{\pi }\]

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