# i find this integral problem very interesting !!! Help on this interesting integral problem ?? Note by Ritvik Choudhary
7 years ago

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It can be solved by GAMMA FUNCTION=integrate(0-infinity)e^-x.x^(n-1)dx for all x>=1 x belongs to Z+!!!

- 6 years, 11 months ago

Although $\int e^{-x^2}\,dx$ can't be expressed in terms of elementary functions, we can evaluate $\int_{-\infty}^{+\infty} e^{-x^2}\,dx$. Doing so yields $\sqrt{\pi}$ (for justification see http://en.wikipedia.org/wiki/Gaussian_integral#Computation).

- 7 years ago

This function is not integrable using the methods we learn till Undergraduate college level. I don't know about what we learn in college...

- 7 years ago

As our function is an even function therefore split the limit of integration from -infinity to +infinity as 2 times 0 to infinity and use Gamma function by making a suitable substitution. It can also be done by converting the problem into polar form.

- 7 years ago

I think ans is 0 .. I think we can solve it using integration by part

- 7 years ago

squareroot of Pi ? ( Error Function)

- 7 years ago

another not-so-cool way is to use gamma function.use the substitution x=root u

- 7 years ago

ya it's cool.you try to find the square of the quantity,with one variable x and the other y.then you integrate them simultaneously,a double integral.It's easy to evaluate once you transform it to polar coordinates.Nice One.Answer is root pi

- 7 years ago

You can also look up this pdf www.stankova.net/statistics2012/doubleintegration.pdf.

- 7 years ago

lower limit is negative infinity..

- 7 years ago