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Math Help - logarithmic function

  1. #1
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    logarithmic function

    how do i show that \frac{d^2}{dx^2}\int_{-1} ^1 {log|x-t|}dt= \int_{-1}^1 \frac{-1}{(x-t)^2}dt is INCORRECT?

    i know that to interchange limit and integral, a function must be uniformly convergent to its limit. but i dont know exactly how to show it.
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  2. #2
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    Quote Originally Posted by Kat-M View Post
    how do i show that \frac{d^2}{dx^2}\int_{-1} ^1 {log|x-t|}dt= \int_{-1}^1 \frac{-1}{(x-t)^2}dt is INCORRECT?

    i know that to interchange limit and integral, a function must be uniformly convergent to its limit. but i dont know exactly how to show it.
    Can you differentiate an absolute value function at every point?
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