Question

Find the value for integral
1/2pi integral over limit 0 to infinity exp(-x2/8) dx

Answer 1

First thing to know is the value of
\[ \int_{-\infty}^{\infty} e^{-x^2} dx \]

Do you know the value of this integral?

Answer 2

My argument is that if you know the value of this integral, we can get to the value of your integral.

Answer 3

I think we should use ILATE formula to integrate it

Answer 4

I don't know what ILATE is but I'll tell you the value is \( \sqrt{\pi} \).

Answer 5

That being the case, what then is the value of
\[ \int_{-\infty}^{\infty} e^{-x^2/a^2} dx \]
You can evaluate it by using a substitution u = x/a

Answer 6

But in option a) 1, b) pi ,c) 2 and d)2pi are given and one of them is correct

Answer 7

We haven't got to your integral yet. We're building up to it.

Answer 8

Basically how use those integral symbol with limit i don't know. That's why I wrote the problem like that

Answer 9

JamesJ, when your done with this question, can you please help me

Answer 10

Your integral,
\[ \frac{1}{2\pi} \int_0^{\infty} e^{-x^2/8} dx = \frac{1}{2\pi}\frac{1}{2} \int_{-\infty}^{\infty} e^{-x^2/8} dx \ \ \ \ \hbox{because the integrand is an even function} \]

Answer 11

...an even function

Answer 12

Therefore if you know how to find the value of
\[ \int_{-\infty}^{\infty} e^{-x^2/a^2} dx \]
you can find the value of your integral. So try the substitution I suggested.

Answer 13

ok i'll try it out with this. thanks