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Q.

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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a

π/2,π/2

b

2/π,3/π

c

0,−4/π

d

4/π,0

answer is D.

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Detailed Solution

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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