# i find this integral problem very interesting !!!

Help on this interesting integral problem ??

Note by Ritvik Choudhary
6 years, 2 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
• Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

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} $\boxed{123}$

## Comments

Sort by:

Top Newest

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, 2 months ago

Log in to reply

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).

- 6 years, 2 months ago

Log in to reply

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

- 6 years, 2 months ago

Log in to reply

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.

- 6 years, 2 months ago

Log in to reply

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

- 6 years, 2 months ago

Log in to reply

squareroot of Pi ? ( Error Function)

- 6 years, 2 months ago

Log in to reply

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

- 6 years, 2 months ago

Log in to reply

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

- 6 years, 2 months ago

Log in to reply

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

- 6 years, 2 months ago

Log in to reply

lower limit is negative infinity..

- 6 years, 2 months ago

Log in to reply

is it 0

- 6 years, 2 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...