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# Edexcel A2 C4 Mathematics June 2016 - Official Thread watch

1. (Original post by BBeyond)
Fair probs should have guessed Camb?
He's not that good.
2. These problems are getting somewhat above c4 standard..
3. (Original post by 13 1 20 8 42)
These problems are getting somewhat above c4 standard..
4. (Original post by Zacken)
3. Using , evaluate: .

Extension: Evaluate .
(Original post by Zacken)
4. Evaluate using a similar substitution to my other integral.

5. Generalise this substitution and prove that it holds for all smoothly behaved when evaluating
Saving these beauties for later
5. (Original post by Euclidean)
Saving these beauties for later
Let me know how you get on.
6. (Original post by Zacken)
4. Evaluate using a similar substitution to my other integral.

5. Generalise this substitution and prove that it holds for all smoothly behaved when evaluating
Ffs misread your first question here and have been trying to integrate ln(1+sinx) instead and getting absolutely nowhere
7. (Original post by Zacken)
If I say , I'm really just making a substitution then . :-)

Well if you call your integral - then you have .

(although that's not quite correct, use that idea).
I've never seen that before. I still don't know what to do though. If I let the original integral = I and mine = J, I have that J = the integral of ln(2) - I? Is that the right idea?
8. (Original post by Zacken)
I just hope if any non-STEPers/maths students/general maths enthusiasts see them they don't get too scared..

I'll throw in a standard that everyone should know to level the balance

9. (Original post by Fudge2)
I've never seen that before. I still don't know what to do though. If I let the original integral = I and mine = J, I have that J = the integral of ln(2) - I? Is that the right idea?

If we let the original integral be , then our substitution gives us:

Which is just: , so you can re-arrange and solve for .
10. (Original post by BBeyond)
Ffs misread your first question here and have been trying to integrate ln(1+sinx) instead and getting absolutely nowhere
Yeah, the mis-read one is a hard one. The definite integral is given in terms of Catalan's constant: .
11. (Original post by Zacken)

If we let the original integral be , then our substitution gives us:

Which is just: , so you can re-arrange and solve for .
Haha I was kinda hoping that was the case! That's really neat though. I got pi/8ln2...?
12. (Original post by Fudge2)
Haha I was kinda hoping that was the case! That's really neat though. I got pi/8ln2...?
Yeah, nothing like this would ever come up on a C4 paper. That's correct, good work!
13. (Original post by Zacken)
Yeah, nothing like this would ever come up on a C4 paper. That's correct, good work!
14. (Original post by Fudge2)
Enjoyed it?
15. (Original post by Zacken)
4. Evaluate using a similar substitution to my other integral.

5. Generalise this substitution and prove that it holds for all smoothly behaved when evaluating
Spoiler:
Show

Wasn't so sure about this one but I got -pi/2(ln2) ? I attached my solution as I'm almost sure this is wrong
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16. (Original post by Zacken)
Enjoyed it?
Yeah! Despite the fact I'll probably never have to use that trick again it was cool...
17. (Original post by 13 1 20 8 42)

Spoiler:
Show

( doesn't look nice lmao)
18. (Original post by BBeyond)
Spoiler:
Show

Wasn't so sure about this one but I got -pi/2(ln2) ? I attached my solution as I'm almost sure this is wrong
Posted from TSR Mobile
Yep, that's fine. But unwieldy but it works. Now try doing the general case.
19. (Original post by Fudge2)
Yeah! Despite the fact I'll probably never have to use that trick again it was cool...
I've used it a hundred times over when doing integration problems, not at C4 level, but you'll see. :-)
20. (Original post by Zacken)
Yep, that's fine. But unwieldy but it works. Now try doing the general case.
Is there a quicker way of doing that? Buzzing with that though ahah didn't even know about this trick until today. I think that might be a bit past my level lol

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