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Questions  

Suppose that f is an odd function and F(x)=axf(t)dt.

Statement-1: F is an even function

Statement-2: aaf(t)dt=0

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a
STATEMENT-1 is True, STATEMENT-2 is True;  STATEMENT-2 is a correct explanation for STATEMENT-1
b
STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
c
STATEMENT-1 is True, STATEMENT-2 is False
d
STATEMENT-1 is False, STATEMENT-2 is True

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detailed solution

Correct option is A

F(x)=∫ax f(t)dt=−∫−a−x f(u)du (u=−t)=∫−a−x f(u)du=∫−aa f(u)du+∫a−x f(u)du=∫a−x f(u)du=F(−x)


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