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HSC 2012 MX1 Marathon #2 (archive) (3 Viewers)

barbernator

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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
 

Timske

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Re: HSC 2012 Marathon :)

isnt it f'(x)/f(x) ?
 

Timske

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Re: HSC 2012 Marathon :)

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

woops
 

barbernator

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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
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?
 
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Carrotsticks

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Re: HSC 2012 Marathon :)

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:

 

barbernator

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Re: HSC 2012 Marathon :)

LOL comments removed deswa and nightweaver hehe
 

Kingportable

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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
 

Timske

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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
x=-2+1/2 do you mean -2.5?
 

deswa1

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Re: HSC 2012 Marathon :)

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?
 

barbernator

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Re: HSC 2012 Marathon :)

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?
 

deswa1

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Re: HSC 2012 Marathon :)

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)
 

Carrotsticks

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Re: HSC 2012 Marathon :)

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...
 

Kingportable

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Re: HSC 2012 Marathon :)

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
 

nightweaver066

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Re: HSC 2012 Marathon :)

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.
 

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