There are two methods to take d/dx [ ∫(adsbygoogle = window.adsbygoogle || []).push({}); _{t=0}^{x}exp(-t^2) dt].

First method: using the relationship of integral and antiderivative, one gets

(exp(-t^2) , from t = 0 to x, so exp(-x^2) - 1.

Second method: the integral is (1/2)sqrt(pi)*erf(t) from 0 to x, which is (1/2)sqrt(pi)*erf(x), and the derivative of this is exp(-x^2).

So, which answer is correct, and what is wrong with the other method?

(Wolfram alpha favors the second answer, but I have another source that favors the first answer.)

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# D/dx[int(0,x) e^(-t^2) dt] : two methods, two answers

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