865Is the answer 0?
Ranadeep Roy YesUpvote·0· Reply ·2014-05-04 06:02:31
If f(x) is an invertible func such that f(x) + f(-x)=2a then ∫a-xa+x f-1(t)dt equals :
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2 Answers
865865Putting x=0, we get f(0)=a. Now, we notice that f(x) is point symmetric about (0, a). That is, if we shift the origin to (0, a) we will get an odd function. Therefore, f-1(a+x)= -f-1(a-x). Hence, the integral will come out to be zero.