Question-90465

Question Number 90465 by Hassen_Timol last updated on 23/Apr/20

Commented by Hassen_Timol last updated on 23/Apr/20

Proof for the last line

Please \dots its quite urgent, please \dots

Commented by abdomathmax last updated on 23/Apr/20

U_{n} = \int_{0}^{1} x^{n} e^{x^{2}} d x \Rightarrow U_{n} = \int_{0}^{1} x^{n - 1} ({x e}^{x^{2}}) d x

b y p a r t s f = x^{n - 1} a n d g^{^{'}} = {x e}^{x^{2}} \Rightarrow

U_{n} = {[\frac{1}{2} x^{n - 1} e^{x^{2}}]}_{0}^{1} - \frac{1}{2} \int_{0}^{1} (n - 1) x^{n - 2} e^{x^{2}} d x

= \frac{1}{2} (e) - \frac{n - 1}{2} \int_{0}^{1} x^{n - 2} e^{x^{2}} d x

= \frac{e}{2} - \frac{n - 1}{2} U_{n - 2} \Rightarrow

U_{n + 2} = \frac{e}{2} - \frac{n + 1}{2} U_{n} t h e r e l a t i o n i s p r o v e d .

Commented by Hassen_Timol last updated on 24/Apr/20

Thank you so much, {it}^{'} s very nice \dots

Be blessed

Commented by Hassen_Timol last updated on 24/Apr/20

But how do you pass from 2 nd to 3 rd line please ?

Commented by mathmax by abdo last updated on 24/Apr/20

i n t e g r a t i o n b y p a r t s

Commented by Hassen_Timol last updated on 24/Apr/20

okay thank you