x Turn on thread page Beta
 You are Here: Home >< Maths

# The Proof is Trivial! watch

1. Problem 202: *
Just a bit of fun. Really not very difficult, but it looks nice
Find:

And hence evaluate:

2. (Original post by bananarama2)
...

(*)

I left out the sub and rearrangement. I completely understand why LOTF does it now. Ask if you want.

[/tex]

Footnote: The only stats I know is S1 and that from reading about QM, so I just basically made it up from what I know
I used IBP as well. Couple of questions/comments:

1) On the line I've added (*) to, haven't you missed out a factor of (1-x) on the denominator.
2) Whilst you might not want to write out the entire sub, just stating which substitution you've used (In this case ) might be nice for readers.

(Also, I just realised - I forgot that the integral should have a factor of 2 added to it (From the initial uniform distribution of x) so the answer is actually supposed to be double what I stated. :O )
3. (Original post by DJMayes)
I used IBP as well. Couple of questions/comments:

1) On the line I've added (*) to, haven't you missed out a factor of (1-x) on the denominator.
2) Whilst you might not want to write out the entire sub, just stating which substitution you've used (In this case ) might be nice for readers.

(Also, I just realised - I forgot that the integral should have a factor of 2 added to it (From the initial uniform distribution of x) so the answer is actually supposed to be double what I stated. :O )
I'll fix that, It's because I made a mistake when I did it on the whiteboard and copied the wrong things down

Okay

I did wonder, because there are two halfs? I wasn't confident enough with my reasoning to say though.
4. (Original post by bananarama2)
I'll fix that, It's because I made a mistake when I did it on the whiteboard and copied the wrong things down

Okay

I did wonder, because there are two halfs? I wasn't confident enough with my reasoning to say though.
It's because you have to take the shorter half, so it's uniformly distributed between 0 and 1/2. The probability density function of this is therefore 2, which gives an extra factor of 2 when doing the integral. The problem was, I moved it to the outside and then had all the integration to do, but forgot to move it back in by the time the integration was done.
5. (Original post by DJMayes)
It's because you have to take the shorter half, so it's uniformly distributed between 0 and 1/2. The probability density function of this is therefore 2, which gives an extra factor of 2 when doing the integral. The problem was, I moved it to the outside and then had all the integration to do, but forgot to move it back in by the time the integration was done.
Yeh, yeh that's what I meant. It was the initial " x<0.5 malarkey" I had to think about most. For some reason stats just doesn't click with me at all.
6. (Original post by bananarama2)
Yeh, yeh that's what I meant. It was the initial " x<0.5 malarkey" I had to think about most. For some reason stats just doesn't click with me at all.

Don't worry, every 6 in 3 people aren't good at statistics.
7. (Original post by joostan)
Problem 202: *
Just a bit of fun. Really not very difficult, but it looks nice
Find:

And hence evaluate:

Solution 202:

Let

Plugging in limits, we get 1.
8. (Original post by DJMayes)
Solution 202:

Let

Plugging in limits, we get 1.
Nice I used the sub but it all amounts to the same thing
9. Solution 202

By inspection, or letting , the answer is

The definite integral is then ln(2).
10. (Original post by james22)
Solution 202

By inspection, or letting , the answer is

The definite integral is then ln(2).
I think you may have made a mistake
http://www.wolframalpha.com/input/?i...nd+e^%28e^e%29
11. (Original post by joostan)
I think you may have made a mistake
http://www.wolframalpha.com/input/?i...nd+e^%28e^e%29
I put the brackets in the wrong place, this is the calculation I did

http://www.wolframalpha.com/input/?i...nd+%28e^e%29^e
12. (Original post by james22)
I put the brackets in the wrong place, this is the calculation I did

http://www.wolframalpha.com/input/?i...nd+%28e^e%29^e
Fair enough
13. what language is this
must be spanish
maybe french
14. (Original post by bananarama2)
I completely understand why LOTF does it now.
Maybe one day, you'll agree on the beauty of this as well...

When an integer, it is a perfect square.

Spoiler:
Show

(by the way I am not posting this as a problem for the thread)
15. (Original post by Abdullahi_3487)
what language is this
must be spanish
maybe french
This beautiful language is maths, one day I hope to speak it as well as LotF, if that is possible
16. (Original post by Lord of the Flies)
Maybe one day, you'll agree on the beauty of this as well...

When an integer, it is a perfect square.

Spoiler:
Show

(by the way I am not posting this as a problem for the thread)

Just curious, to prove this would it be a **/*** problem?

Edit: Also, why doesn't your picture have a Euro coin falling towards the Eastern side?
17. I like the way my problems stir up so much trouble
18. (Original post by Zakee)
Just curious, to prove this would it be a **/*** problem?
It is a */**, but a difficult one.

(the joke was that it requires a mathematical argument which I love and which bananarama despises - I'll let you figure out what it is from the picture)
19. (Original post by Lord of the Flies)
It is a */**, but a difficult one.

(the joke was that it requires a mathematical argument which I love and which bananarama despises - I'll let you figure out what it is from the picture)
Spoiler:
Show
Unfortunately those stairs are very unlikely to be long enough for the analogy to be apt.
20. (Original post by Lord of the Flies)
Maybe one day, you'll agree on the beauty of this as well...

When an integer, it is a perfect square.

Spoiler:
Show

(by the way I am not posting this as a problem for the thread)
Infinite Descent?

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 22, 2018
Today on TSR

### Boyfriend slept with someone else

...we were on a break

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams