# Thread: HSC 2012 Marathon :)

1. ## Re: HSC 2012 Marathon :)

why doesn't the general formula work to integrate

integral e^ln(x) = e^f(x)/f'(x) = e^ln(x)/1/x = x^2 =/= x^2/2

i know that it can just be simplified to x, but im wondering why the formula doesn't work

2. ## Re: HSC 2012 Marathon :)

Any ideas though?

3. ## Re: HSC 2012 Marathon :)

isnt it f'(x)/f(x) ?

4. ## Re: HSC 2012 Marathon :)

Originally Posted by nightweaver066
lol
did i just make an extremely rookie error?

5. ## Re: HSC 2012 Marathon :)

integral e^lnx = f'(x)/f(x) = 1/x

woops

6. ## Re: HSC 2012 Marathon :)

Originally Posted by Timske
integral e^lnx = f'(x)/f(x) = 1/x

woops
shitballs

I just got on the forums again and I see this..

7. ## Re: HSC 2012 Marathon :)

Originally Posted by Timske
integral e^lnx = f'(x)/f(x) = 1/x

woops
ok now u guys can lol at me, does that give me permission to lol at this?

8. ## Re: HSC 2012 Marathon :)

Originally Posted by barbernator
why doesn't the general formula work to integrate

integral e^ln(x) = e^f(x)/f'(x) = e^ln(x)/1/x = x^2 =/= x^2/2

i know that it can just be simplified to x, but im wondering why the formula doesn't work
but 4srs, i know that e^ln(x)=x. but why can u not use e^f(x)/f'(x) to integrate instead. Is it something to do with the domain of the function?

9. ## Re: HSC 2012 Marathon :)

Originally Posted by deswa1
Oooh, if you could find it, can you post it again. A nice question that I remember you posting was how to integrate 1/1+tan^n(x) between 0 and pi/2 but that needs 4U techniques...
I don't remember that question... Anyway here it is:

10. ## Re: HSC 2012 Marathon :)

LOL comments removed deswa and nightweaver hehe

11. ## Re: HSC 2012 Marathon :)

Originally Posted by barbernator
but 4srs, i know that e^ln(x)=x. but why can u not use e^f(x)/f'(x) to integrate instead.
because e^lnx = x thats why hahah

12. ## Re: HSC 2012 Marathon :)

John Fitzpatrick 3U Mathematics 25(c) Question 3

A particle movies in a straight line. At time t seconds, its displacement x cm from a fixed poin O in the line is given by x=5sin((pi/2)T + pi/6). Express the acceleration in terms of x only and hence show that the motion is simple harmonic. Find:

iii) The speed when x=-2+1/2
iv) the acceleration when x = -2 + 1/2

13. ## Re: HSC 2012 Marathon :)

Originally Posted by Kingportable
John Fitzpatrick 3U Mathematics 25(c) Question 3

A particle movies in a straight line. At time t seconds, its displacement x cm from a fixed poin O in the line is given by x=5sin((pi/2)T + pi/6). Express the acceleration in terms of x only and hence show that the motion is simple harmonic. Find:

iii) The speed when x=-2+1/2
iv) the acceleration when x = -2 + 1/2
x=-2+1/2 do you mean -2.5?

14. ## Re: HSC 2012 Marathon :)

Originally Posted by barbernator
LOL comments removed deswa and nightweaver hehe
Ahh you noticed. I removed it because I didn't read your question properly and I didn't want to look like a retard if I was wrong. What is your question?

15. ## Re: HSC 2012 Marathon :)

Originally Posted by deswa1
Ahh you noticed. I removed it because I didn't read your question properly and I didn't want to look like a retard if I was wrong. What is your question?
the question is, why when integrating e^ln(x) through both methods e^f(x)/f'(x) and x yield different results?

16. ## Re: HSC 2012 Marathon :)

Originally Posted by barbernator
the question is, why when integrating e^ln(x) through both methods e^f(x)/f'(x) and x yield different results?
How can you integrate e^ln(x) using this. If f(x)=ln(x), then f'(x)=1/x. Therefore to use this form, you would have to be integrating (1/x)(e^ln(x)) not just e^ln(x)

17. ## Re: HSC 2012 Marathon :)

Originally Posted by barbernator
the question is, why when integrating e^ln(x) through both methods e^f(x)/f'(x) and x yield different results?
How did you get the bolded part? That is only applicable if f'(x) is a constant...

18. ## Re: HSC 2012 Marathon :)

Originally Posted by Timske
x=-2+1/2 do you mean -2.5?
yes, btw i tried using x''=-n^2 . x and v^2=n^2 . (a^2 + x^2)

My problem with differentiation from the displacement was that i didn't have a value for t

19. ## Re: HSC 2012 Marathon :)

Originally Posted by deswa1
Ahh you noticed. I removed it because I didn't read your question properly and I didn't want to look like a retard if I was wrong. What is your question?
Same, then i realised his question is troll.

20. ## Re: HSC 2012 Marathon :)

Originally Posted by Carrotsticks
I don't remember that question...
The question that you got from one of your students; that i indirectly sent you :P

21. ## Re: HSC 2012 Marathon :)

Originally Posted by nightweaver066
The question that you got from one of your students; that i indirectly sent you :P
Oh right yes yes I remember now.

Here's an interesting question:

A and B are two positive integers such that A > B and A =/= B.

Now consider A^B and B^A.

Which one is larger? Do any conditions need to be imposed to satisfy each inequality?

22. ## Re: HSC 2012 Marathon :)

Originally Posted by nightweaver066
Same, then i realised his question is troll.
nah it wasn't a troll, i have just had my definition of integration wrong the whole time for exponents lol. its only e^f(x)/f'(x) for linear factors.... my bad

23. ## Re: HSC 2012 Marathon :)

Originally Posted by Carrotsticks
Oh right yes yes I remember now.

Here's an interesting question:

A and B are two positive integers such that A > B and A =/= B.

Now consider A^B and B^A.

Which one is larger? Do any conditions need to be imposed to satisfy each inequality?
Consider A=5, B=2, B^A>A^B. Now consider A=3, B=2, A^B>B^A. Therefore conditions must be placed to satisfy the inequalities. Unfortunately I don't have time now to work it out- I'll try it tomorrow though because it looks cool

24. ## Re: HSC 2012 Marathon :)

Lol plox someone help me solve this question, its driving me crazy!

John Fitzpatrick 3U Mathematics 25(c) Question 3

A particle movies in a straight line. At time t seconds, its displacement x cm from a fixed poin O in the line is given by x=5sin((pi/2)T + pi/6). Express the acceleration in terms of x only and hence show that the motion is simple harmonic. Find:

iii) The speed when x=-2 1/2 or x = - 5/2
iv) the acceleration when x = -2 1/2 or x = - 5/2

25. ## Re: HSC 2012 Marathon :)

Originally Posted by barbernator
nah it wasn't a troll, i have just had my definition of integration wrong the whole time for exponents lol. its only e^f(x)/f'(x) for linear factors.... my bad

I wouldn't use that formula, stick to the simple $\int f'(x)e^{f(x)} dx = e^{f(x)} + c$ and stick to 'balancing' to integrate.

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