0-1-x-d-e-x-2-how-it-solve-

Question Number 151738 by tabata last updated on 22/Aug/21

\int_{0}^{1} x d (e^{x^{2}})

h o w i t s o l v e

Answered by Olaf_Thorendsen last updated on 22/Aug/21

I = \int_{0}^{1} x d (e^{x^{2}})

I = {[{x e}^{x^{2}}]}_{0}^{1} - \int_{0}^{1} e^{x^{2}} d x

I = e - \frac{\sqrt{π}}{2} {[erfi (x)]}_{0}^{1}

I = e - \frac{\sqrt{π}}{2} erfi (1)

erfi (z) = \frac{2}{\sqrt{π}} \underset{n = 0}{\sum^{\infty}} \frac{z^{2 n + 1}}{(2 n + 1) n!}

I = e - \underset{n = 0}{\sum^{\infty}} \frac{1}{(2 n + 1) n!}

Commented by Olaf_Thorendsen last updated on 22/Aug/21

I \approx e - 1, 462651746

I \approx 1, 255630082