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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... its quite urgent, please...
ProofforthelastlinePleaseitsquiteurgent,please
Commented by abdomathmax last updated on 23/Apr/20
U_n   =∫_0 ^1  x^n  e^x^2  dx  ⇒U_n =∫_0 ^1  x^(n−1)  (xe^x^2  )dx  by parts f=x^(n−1)  and g^′ =xe^(x^2  )  ⇒  U_n =[(1/2)x^(n−1)  e^x^2  ]_0 ^1  −(1/2)∫_0 ^1  (n−1)x^(n−2)  e^x^2  dx  =(1/2)(e)−((n−1)/2) ∫_0 ^1  x^(n−2)  e^x^2  dx  =(e/2)−((n−1)/2) U_(n−2)  ⇒  U_(n+2) =(e/2)−((n+1)/2) U_n    the relation is proved.
Un=01xnex2dxUn=01xn1(xex2)dxbypartsf=xn1andg=xex2Un=[12xn1ex2]011201(n1)xn2ex2dx=12(e)n1201xn2ex2dx=e2n12Un2Un+2=e2n+12Untherelationisproved.
Commented by Hassen_Timol last updated on 24/Apr/20
Thank you so much, it′s very nice...  Be blessed
Thankyousomuch,itsveryniceBeblessed
Commented by Hassen_Timol last updated on 24/Apr/20
But how do you pass from 2nd to 3rd line please ?
Buthowdoyoupassfrom2ndto3rdlineplease?
Commented by mathmax by abdo last updated on 24/Apr/20
integration by parts
integrationbyparts
Commented by Hassen_Timol last updated on 24/Apr/20
okay thank you
okaythankyou

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