Aproximari

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Bogdan Cebere
Thales
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Aproximari

Post by Bogdan Cebere »

Sa se calculeze \( \int_0^1 x^x dx \) cu trei zecimale exacte.
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aleph
Thales
Posts: 123
Joined: Mon Dec 24, 2007 2:06 am

Post by aleph »

Sunt suficienţi primii 4 termeni ai dezvoltării (vezi Fihtenholţ)

\( \int_0^1 x^x dx = \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n^n} \)

adică \( 1-1/4+1/27-1/256 \)
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