Help, Integration by Parts Reduction Method

C

crimsoneyelion

New member
Joined
Oct 4, 2005
Messages
7
Please, I've been stuck on one problem for 5 hours, which has never happened to me before, I've always gotten these so easy until now. But I'm lost on this one, so any help would be greatly appreciated. The problem is:
Find the integral from 0 to 1 of xe^(-x^1/2) dx. I can't get a u and dv that will cancel out one of the problems, nor can I find a substition that makes the problem any easier.
 
You may have to get a bit creative.

Maybe it would help if you wrote it like this:

x*e<sup>-sqrt(x)</sup> = {-2*x<sup>3/2</sup>}*{[e<sup>-sqrt(x)</sup>]/[-2*sqrt(x)]}

Now, ask yourself, what's (d/dx)(e<sup>-sqrt(x)</sup>)
 
My calcultor shows: -2e^(-x^(1/2)) ( x^(3/2) + 3x + 6x^(1/2) +6 ), and when 0 and 1 are plugged in, 12 - 32/e, but I have no clue how to get there.
 
That substitution gets you to 3/2 the integral of u * e ^ (-sqrt x) du, but where from there? Sorry for asking so many questions, I'm just mentally shot, I stayed up till 3 trying to figure this out.
 
crimsoneyelion said:
I've actually tryed that route before, but it got me nowhere.
Click to expand...
You gave up too soon. Do it again, exactly the same way.
 
When I did that, I used {e^(-sqrtx)/-2sqrtx) as my dv, which made v e^-sqrtx, u was x^(3/2) and du was 3sqrtx/2. But that made the problem e^-sqrtx * x^(3/2) - the integral of e^-sqrtx * 3sqrtx/2 dx, I still have two variables in the integral, am I missing something?
 
I think this one takes three or four applications of integration by parts. There is a reason it is called a "reduction method". It won't necessarily solve things right away, but it will bring you closer on each lap around the track.
 
Thank you so much! I finally figured it out, I'm so happy. Ugh, I'm glad i remembered a trick our teacher taught us, the integral of e^-sqrtx = -2e^-sqrtx(sqrtx +1)
 
You must log in or register to reply here.
Top