2015 Countdown Problem #15: Palindrome Integration

Algebra Level 5

Let \(x\) be a real number and \(f(x)\) be a real-valued function on \(x\) such that \(f(x)\) is:

  • the next palindrome larger than \(x\) (if \(x\) is not a palindrome); or

  • \(x\) (if \(x\) is a palindrome).

For example, \(f(1001)=1001\),\(f(1001.01)=f(1002)=1111\).


\[A=\int _{ 999 }^{ 2015 }{ f(x) \mbox{ } dx } \]


Find the value of \(\frac{A}{B}\).

This problem is part of the set 2015 Countdown Problems.


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