rishi -- since you are doing integral problems

by MaxEntropy_Man Mon Apr 15, 2013 1:12 pm

try this somewhat difficult but doable integral which occurs in statistical mechanics frequently, and statistics in general.

e^(-x^2); integration limits 0 to infinity.

no googling.

by Rishi Mon Apr 15, 2013 3:30 pm

MaxEntropy_Man wrote:try this somewhat difficult but doable integral which occurs in statistical mechanics frequently, and statistics in general.

e^(-x^2); integration limits 0 to infinity.

no googling.

Max,

The teacher has not covered anything about infinite intervals.

I looked at the chapter in a text book on improper integrals.

infinity t
∫(e ^ -(x^2) )dx can be written as lim t ---> infinity ∫(e ^ -(x^2)) dx

0 0

we know that

d/dt of

t
∫(e ^ -(x^2) )dx = e ^ -(t ^2)

0

I also know that lim t ---> infinity of e ^ -(x ^ 2) which is equal to infinity

and t ---> -infinity of e ^ (x ^2) which is equal to zero.

I have to tie all these facts together.

This is as far as I can go at this point.

by Rishi Mon Apr 15, 2013 9:00 pm

Max,

It tried to first find the indefinite integral of e ^ (-(x^2))

I substituted u= -(x^2), then du= -2xdx

There is no way to rewrite the integrand in terms of the e ** (something) *(-2xdx)

by MaxEntropy_Man Mon Apr 15, 2013 9:17 pm

Rishi wrote:Max,

It tried to first find the indefinite integral of e ^ (-(x^2))

I substituted u= -(x^2), then du= -2xdx

There is no way to rewrite the integrand in terms of the e ** (something) *(-2xdx)

rishi,

it is not possible to get a closed form expression for the indefinite integral but it is possible to evaluate the definite integral exactly but it requires the use of a trick. has the professor addressed double integrals yet? this is not a double integral, but the easiest way to do it is to convert it into one.

by Rishi Mon Apr 15, 2013 10:28 pm

Max,

The course I am taking is Calculus I. It is single variable calculus.

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rishi -- since you are doing integral problems

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