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# The Proof is Trivial! Watch

1. Spoiler:
Show
Just read about the MIT integration bee! Turns out the integrals on there aren't as hard as the ones on here...

The qualifying round is basically having 20 minutes to solve as many of a list of 25 integrals as possible and then, in the finals, you do the same but neck and neck with someone else of chalk boards side by side. Most of them seem mad easy

Here's a link if anyone's interested... or want to post more on here!

Problem 174*

Evaluate

Problem 175*

Evaluate

Problem 176*

Evaluate

Problem 177*

Evaluate

Problem 178*

Evaluate

Problem 179*

Evaluate

Problem 180*

Evaluate

Problem 181*

Evaluate

Problem 182*

Evaluate

Problem 183*

Evaluate

...and finally, this one was tie breaker between the top two (how it took them a whole minute I have no idea! You can do this **** in your head )

Problem 184*

Evaluate
2. Solution 174

Let

Solution 175

Let

Solution 177

Solution 180

I'll leave the rest, 183 looks like an algebraic mess
3. Solution 175:

I =

Let

Re-arranging, we get:

The first part of this is a standard arcsin integral and yields . Let's look at the second part:

Let

4. (Original post by Felix Felicis)
Problem 171, 172
Felix you need to relable your questions, there already is a 171

Problem 185*

Find all such that:

Problem 186*

A nice problem. Prove/disprove that there exists such that:

means applied times in this case.

Well, to those who were unhappy about the lack of (*)'s, you now have loads. Go go go go!
5. (Original post by Jkn)

Problem 178*

Evaluate
Are you sure the upper limit is supposed to be 2? Otherwise the integral is not defined for real numbers past 1...
6. (Original post by Felix Felicis)
Solution 174

Let

In light of it being a "speed" competition, allow me to direct you toward my solution

Solution 174
(2)

Let ,

7. (Original post by DJMayes)
Are you sure the upper limit is supposed to be 2? Otherwise the integral is not defined for real numbers past 1...
Sorry typo, 'tis now fixed (that's what you get for setting two questions at once)
8. (Original post by Jkn)
In light of it being a "speed" competition, allow me to direct you toward my solution

Solution 174
(2)

Let ,

It takes like 10 seconds less Neat, nonetheless
9. (Original post by Lord of the Flies)
Felix you need to relable your questions, there already is a 171

Problem 185*

Find all such that:

Problem 186*

A nice problem. Prove/disprove that there exists such that:

means applied times in this case.

Well, to those who were unhappy about the lack of (*)'s, you now have loads. Go go go go!
No way these look exactly like the functional equations questions you get in Core 4!
Spoiler:
Show
Lol jk functional equations are not * questions
10. (Original post by Felix Felicis)
It takes like 10 seconds less Neat, nonetheless
Meh

Please post some interesting series and/or integration questions
11. (Original post by Jkn)
Meh

Please post some interesting series and/or integration questions
I'll have a look around and see what I have

Edit: I thought the first integral you posted was and I thought no way in hell can anyone do that in 20 minutes
12. (Original post by Jkn)
Lol jk functional equations are not * questions
Yes they are. In fact a lot of functional equations only require GCSE knowledge.
13. (Original post by Lord of the Flies)
Yes they are. In fact a lot of functional equations only require GCSE knowledge.
But the concept of a function isn't introduced until a-level
14. (Original post by Jkn)
But the concept of a function isn't introduced until a-level
15. (Original post by Jkn)
But the concept of a function isn't introduced until a-level
I'm pretty sure I've seen function-related GCSE questions on the maths forum but whatever. Anyhow, can we stop cluttering the thread with this chatter, both questions are * the end.
16. (Original post by Jkn)

Problem 178*

Evaluate
Let

x = 0 so u = 0, coshu = 1, x = 2 so coshu = 3

Finally plugging those in I get 1192/45, although this isn't really a nice answer...
17. (Original post by Lord of the Flies)
I'm pretty sure I've seen function-related GCSE questions on the maths forum but whatever.
Yes, but the way GCSEs are taught means they wouldn't have a clue what a function was even if they do stuff related to them....
18. (Original post by DJMayes)
Let

x = 0 so u = 0, coshu = 1, x = 2 so coshu = 3

Finally plugging those in I get 1192/45, although this isn't really a nice answer...
Or u =1+x^3 ?
19. (Original post by Felix Felicis)
Edit: I thought the first integral you posted was and I thought no way in hell can anyone do that in 20 minutes
Lightweight, you can get it form applying integration by parts to the other one by integrating (and differentiating the denominator) and then evaluating a fairly trivial other part with a tanx substitution
20. (Original post by bananarama2)
Or u =1+x^3 ?
Hyperbolics are more fun.

(What answer do you get with that sub though?)

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