Definite integral (1~∞) x*e^-3x dx
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Definite integral (1~∞) x*e^-3x dx

[From: ] [author: ] [Date: 11-10-20] [Hit: ]
......
I know how to solve but the definite integral to 1 to infinite has thrown me off. Thank you for all the help.

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int (x * e^(-3x)) dx

= (-1/9)(3x + 1) e^(-3x) + C

sub in limits

= (-1/9)(3∞ + 1) e^(-3∞) - (-1/9)(3(1) + 1) e^(-3(1))

with the first group

the limit as x -> ∞ of e^(-3x) is 0

therefore,
= 0 + (1/9)(4) e^-3
= (4/9) e^-3

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That problem just looks like random symbols, Idk how the heck to figure that out
1
keywords: infin,integral,Definite,dx,Definite integral (1~∞) x*e^-3x dx
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