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# Interesting problem. watch

1. It has a cool answer.
2. (Original post by Louisb19)

Off the top of my head, I can think of two ways to do this:

DUTIS:
Spoiler:
Show

.

Then

Integrating: , take to see that and hence .

Then our integral is

Laplace transforms:
Spoiler:
Show
3. (Original post by Zacken)
Off the top of my head, I can think of two ways to do this:

DUTIS:
Spoiler:
Show

.

Then

Integrating: , take to see that and hence .

Then our integral is
Laplace transforms:
Spoiler:
Show
It's a pretty cool answer isn't it.
4. (Original post by Louisb19)
It's a pretty cool answer isn't it.
Indeed, can you hazard a guess as to what is?
5. (Original post by Zacken)
Indeed, can you hazard a guess as to what is?
I'd guess since (I think?)

It would be
6. (Original post by Louisb19)
I'd guess since (I think?)

It would be
Precisely. so is an even function.

?
8. (Original post by Zacken)
Off the top of my head, I can think of two ways to do this:

DUTIS:
Spoiler:
Show

.

Then

Integrating: , take to see that and hence .

Then our integral is

Laplace transforms:
Spoiler:
Show
the Laplace approach is not quite correct
9. (Original post by TeeEm)
the Laplace approach is not quite correct
Is this correct (sorry, my Laplace is horridly rusty):

10. (Original post by Gregorius)

?
Is this just using
Spoiler:
Show
parts with and with a quick for the resulting integral?
11. (Original post by Louisb19)

You might like this. You come up with quite a few interesting problems, so you can post them there in the future!
12. (Original post by Zacken)
Is this correct (sorry, my Laplace is horridly rusty):

I just got back ...
food first!
Then I will write and post the method
13. (Original post by TeeEm)
I just got back ...
food first!
Then I will write and post the method
Bon appetit!
14. (Original post by Zacken)
Bon appetit!
here is the one and another 3 for the interest of whoever cares

Attachment 475265475267Attachment 475265475267475260[attach]4.752654752674753e+23[/attach]

I posted earlier another integral problem here
http://www.thestudentroom.co.uk/show....php?t=3327325

Maybe this is easy to be done now
Attached Images

15. (Original post by TeeEm)
here is the one and another 3 for the interest of whoever cares

Attachment 475265475267Attachment 475265475267475260[attach]4.752654752674753e+23[/attach]

I posted earlier another integral problem here
http://www.thestudentroom.co.uk/show....php?t=3327325

Maybe this is easy to be done now
Many thanks!
16. (Original post by Zacken)
Is this just using
Spoiler:
Show
parts with and with a quick for the resulting integral?
Looks about right; what is amusing in the context of the original question is the actual value of the answer...

Unfortunately the pattern does not continue for

for n in general...
17. (Original post by Gregorius)
Looks about right; what is amusing in the context of the original question is the actual value of the answer...Unfortunately the pattern does not continue forfor n in general...

Interestingly enough we do have that becomes
18. (Original post by Gregorius)
Looks about right; what is amusing in the context of the original question is the actual value of the answer...

Unfortunately the pattern does not continue for

for n in general...
I'll be back in half an hour or so, I'm going to play around with that integral and see if I can any nice recurrences or patterns! Thanks for this!

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