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 Let f be a real-valued function satisfying f(x)+f(x+4)=f(x+2)+f(x+6)  then  xx+8f(t)dt is 

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a
A function in terms of x
b
constant function
c
Periodic function
d
Depends on x

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detailed solution

Correct option is B

Given that f(x)+f(x+4)=f(x+2)+f(x+6)----(1) Replacing x by x+2, we get f(x+2)+f(x+6)=f(x+4)+f(x+8)----(2) From equations ( 1 ) and ( 2 ), we get f(x)=f(x+8)----(3) or ∫xx+8 f(t)dt=∫08 f(t)dt= constant


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