i find this integral problem very interesting !!!

Help on this interesting integral problem ??

#HelpMe! #MathProblem #Math

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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

A Former Brilliant Member - 7 years, 11 months ago

lower limit is negative infinity..

Ritvik Choudhary - 7 years, 11 months ago

is it 0

A Former Brilliant Member - 7 years, 11 months ago

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

Nishant Sharma - 7 years, 11 months ago

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

A Former Brilliant Member - 7 years, 11 months ago

squareroot of Pi ? ( Error Function)

Ahmed Taha - 7 years, 11 months 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.

Anila Tanoli - 7 years, 11 months 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...

Rohan Rao - 7 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).

Clifford Wilmot - 7 years, 11 months ago

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 - 7 years, 11 months ago

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

Anmol Agarwal - 7 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$