i find this integral problem very interesting !!!

Help on this interesting integral problem ??

Note by Ritvik Choudhary
6 years, 2 months ago

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4 votes

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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 - 6 years, 2 months ago

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Although ex2dx\int e^{-x^2}\,dx can't be expressed in terms of elementary functions, we can evaluate +ex2dx\int_{-\infty}^{+\infty} e^{-x^2}\,dx. Doing so yields π\sqrt{\pi} (for justification see http://en.wikipedia.org/wiki/Gaussian_integral#Computation).

Clifford Wilmot - 6 years, 2 months 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 - 6 years, 2 months 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 - 6 years, 2 months ago

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

Anmol Agarwal - 6 years, 2 months ago

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squareroot of Pi ? ( Error Function)

Ahmed Taha - 6 years, 2 months ago

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

Aahitagni Mukherjee - 6 years, 2 months ago

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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

Aahitagni Mukherjee - 6 years, 2 months ago

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

Nishant Sharma - 6 years, 2 months ago

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lower limit is negative infinity..

Ritvik Choudhary - 6 years, 2 months ago

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is it 0

Brilliant Member - 6 years, 2 months ago

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