definite integral

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If f(x) is an invertible func such that f(x) + f(-x)=2a then âˆ«_a-x^a+x f^-1(t)dt equals :

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Soumyadeep Basu ·2014-05-03 10:14:58

Is the answer 0?

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Ranadeep Roy Yes
Upvote·0· Reply ·2014-05-04 06:02:31
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865

Soumyadeep Basu ·2014-05-04 07:44:35

Putting 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.

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definite integral

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