×

# i find this integral problem very interesting !!!

Help on this interesting integral problem ??

Note by Ritvik Choudhary
4 years, 6 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} $$\boxed{123}$$

Sort by:

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

- 4 years, 6 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+!!!

- 4 years, 6 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).

- 4 years, 6 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...

- 4 years, 6 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.

- 4 years, 6 months ago

squareroot of Pi ? ( Error Function)

- 4 years, 6 months ago

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

- 4 years, 6 months ago

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

- 4 years, 6 months ago

lower limit is negative infinity..

- 4 years, 6 months ago

is it 0

- 4 years, 6 months ago

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

- 4 years, 6 months ago