I am trying to get the inverse of: $$g(x) = \int _a ^x h(t) dt$$ That is, I want to find a general expression for $g^{-1}(x)$ and was wondering whether there are theorems I can apply. Thanks
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No, there isn't such an expression. Not even for $g(x)$. – Aug 10 '16 at 18:49
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4Possible dupilcate of: http://math.stackexchange.com/questions/1467784/inverse-of-a-functions-integral/ – shalop Aug 10 '16 at 18:50
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Did you perhaps mean $$g(x) = \int_a^x h(t)dt$$? – Nex Aug 10 '16 at 18:56
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yes Nex thanks so much, I edited the question – splinter Aug 10 '16 at 19:16
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Under some additional conditions, you have $g^{-1}(y) = a + \int_0^y (g^{-1})'(z) dz$ ... I am not sure that it is useful... – user251257 Aug 10 '16 at 20:44
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it actually seems to be an exact duplicate – george Aug 10 '16 at 21:32
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yes it's a duplicate, fully agree. Didn't see it before, sorry about that – splinter Aug 12 '16 at 10:30