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
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Aahitagni Mukherjee
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4 years, 1 month 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+!!!
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Subhrodipto Basu Choudhury
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4 years, 1 month ago

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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).
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Clifford Wilmot
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4 years, 1 month ago

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This function is not integrable using the methods we learn till Undergraduate college level. I don't know about what we learn in college...
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Rohan Rao
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4 years, 1 month ago

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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.
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Anila Tanoli
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4 years, 1 month ago

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squareroot of Pi ? ( Error Function)
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Ahmed Taha
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4 years, 1 month ago

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another not-so-cool way is to use gamma function.use the substitution x=root u
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Aahitagni Mukherjee
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4 years, 1 month ago

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You can also look up this pdf www.stankova.net/statistics2012/doubleintegration.pdf.
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Nishant Sharma
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4 years, 1 month ago

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lower limit is negative infinity..
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Ritvik Choudhary
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4 years, 1 month ago

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TopNewestya 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 – Aahitagni Mukherjee · 4 years, 1 month 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+!!! – Subhrodipto Basu Choudhury · 4 years, 1 month ago

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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). – Clifford Wilmot · 4 years, 1 month ago

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This function is not integrable using the methods we learn till Undergraduate college level. I don't know about what we learn in college... – Rohan Rao · 4 years, 1 month ago

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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. – Anila Tanoli · 4 years, 1 month ago

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squareroot of Pi ? ( Error Function) – Ahmed Taha · 4 years, 1 month ago

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another not-so-cool way is to use gamma function.use the substitution x=root u – Aahitagni Mukherjee · 4 years, 1 month ago

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You can also look up this pdf

www.stankova.net/statistics. – Nishant Sharma · 4 years, 1 month ago2012/doubleintegration.pdfLog in to reply

lower limit is negative infinity.. – Ritvik Choudhary · 4 years, 1 month ago

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– Brilliant Member · 4 years, 1 month ago

is it 0Log in to reply

I think ans is 0 .. I think we can solve it using integration by part – Anmol Agarwal · 4 years, 1 month ago

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