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Expert: Alon Mandes - 7/21/2008


Question
How do you evaluate this definite Integral : Integral of (x^2)*e^(-x^2) with limits from 0 to 1?
I tried to use the following technique but I could not do it:
letting u = x^2, du = 2xdx
1/2du = xdx;
substituting everything back is where I got stuck.


Answer
If you set u=x^2 the integrand becomes (1/2)*[sqrt(u)e^-u].
From the table of integrals you find :
Int[sqrt(u)e^(-au)du]=(1/a)sqrt(u)e^(au)+i*sqrt(pi)/(2*a^(3/2))*
Erf(i*sqrt(au)). where i=sqrt(-1) &
Erf(u)=[2/sqrt(pi)]*Int[e^(-t^2)] t from 0 to u.
Set a=-1, you get : Int[x^2e^(-x^2)]=-sqrt(u)*e^(-u)-Erf(u).
x goes from 0 to 1, & so u goes from 0 to 1. So now ,
then answer will be : -1/e-Erf(1)+Erf(0).
Here's a link for the Erf table :
http://controls.engin.umich.edu/wiki/images/c/c4/Table_Erf.pdf

Alon.

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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