integration question (1 Viewer)

[polythenepam]

hey i need help
the question is
integrate :
(Ln(x^2-4))/(x^2-4)^(1/2) dx

before that it asks to show the integral of
x/(x^2-4)dx = (x^2-4)^1/2

 

[ngai]

(Ln(x^2-4))/(x^2-4)^(1/2) dx

sure thats typed correctly?

 

[polythenepam]

yeeh im sure.. to clarify :
the integral of :
"[Ln of (x squared minus 4)] divided by [square root of (x squared minus 4)]"

 

[HayleeKate]

I beg to differ? I've checked and re-checked several times because I'd back yourself over me, Slide, BUT...
u=sqrt(x^2-4)
du=1/2.2x.(x^2-4)^(1/2)
=x/sqrt(x^2-4)
doesnt it? where does your 2x disappear too? Do I not understand?

Also, considering the first part of the question asks you to show the integral of x/sqrt(x^2-4)... i'd suggest you ought to be using this?

 

[haboozin]

mmmm currently ngai is top of the state for last yr....
so i would trust everything he says

also your integration cant be solved with high school math...


Integrate

Result

 

[martin]

for the previous integral I don't think the answer is right

int(x/(x^2-4))dx = ?

let u=x^2-4, then du = 2 x dx so x dx= du/2

so int(x/(x^2-4))dx
= int(1/2 1/u)du
= 1/2 ln(u) + C
= 1/2 ln(x^2-4) + C
= ln(sqrt(x^2-4)) + C

But how this helps us for the desired integral I don't know. Are you sure you typed it in right or were there any limits provided?

 

[polythenepam]

hmm yeeh there were limits
8^1/2 and 5^1/2
i dont think that makes a difference tho
well yeeh my friend asked me this question so maybe he took it down wrong.. hopefully it's wrong.. no wonder its so screwed
anyway thnx for all ur help

 

[KFunk]

Limits definately make a difference...

 

[FinalFantasy]

hmm yeeh there were limits
8^1/2 and 5^1/2
i dont think that makes a difference tho
well yeeh my friend asked me this question so maybe he took it down wrong.. hopefully it's wrong.. no wonder its so screwed
anyway thnx for all ur help

limits make a huge difference... some ppl just post integration questions without putting the full question in, and we waste lots of time doing it and gain no result lol:\

 

[Antwan23q]

before that it asks to show the integral of
x/(x^2-4)dx = (x^2-4)^1/2

Geez, that is totaly wrong!
integration of x/(x^2-4) is.... 1/2ln|x^2-4|

the derative of (x^2-4)^1/2 = x/((x^2-4)^1/2))


u obviously forgot the the square root infront of the (x^2-4)

that should help i guess

 

[Antwan23q]

Also, id thought you would use trig substitues like x=2secθ

 

[Antwan23q]

good point, i just tried

 

[polythenepam]

yeeh they make a difference to the overall answer but u cant use those limits unless u can get the indefinite integral first
ahh well looks like u cant integrate it anyway

 

[~ ReNcH ~]

mmmm currently ngai is top of the state for last yr....
so i would trust everything he says

also your integration cant be solved with high school math...


Integrate

Result

Where did you get that result from?...do you have an integral calculator or something?

 

[haboozin]

Where did you get that result from?...do you have an integral calculator or something?

yea math.com
this integral is beyond our syllabus

 

[HayleeKate]

this question is a filthy wench.
I tried int by parts first off, thought that would work after the first part of the question, but ended up going around in circles [but not enough to get a recurrence].
The substitution never works out properly. I cant find a similar example in any of my textbooks either.

PS Slide, I was scared to doubt you. It was a much nicer question your method anyway!

 

[ngai]

limits make a huge difference... some ppl just post integration questions without putting the full question in, and we waste lots of time doing it and gain no result lol:\

I AGREE...which is why i feed questions into maple before trying myself

hmm yeeh there were limits
8^1/2 and 5^1/2
i dont think that makes a difference tho
well yeeh my friend asked me this question so maybe he took it down wrong.. hopefully it's wrong.. no wonder its so screwed
anyway thnx for all ur help

maple still cant do it, so im pretty sure u wont need to do it in the hsc

 

[Antwan23q]

You cannot do this question with high school mathematics.

 

[who_loves_maths]

Originally Posted by polythenepam
hey i need help
the question is
integrate :
(Ln(x^2-4))/(x^2-4)^(1/2) dx

before that it asks to show the integral of
x/(x^2-4)dx = (x^2-4)^1/2

i just had this question asked of me last week by a fellow student who was looking at past papers from a Catholic school's trial. (i think he got it through a tutor or something).
anyways, the point this question is misplaced at the HSC level and the integral cannot be found using high school mathematics, even if the integral is a definite integral. unless you know what Polylogarithmic functions are, then it can't be done.

if i remember correctly you are suppose to find its definite integral between sqrt(5) and sqrt(8)... i think... and you're suppose to express it in exact form ---> which leads me to believe the integral is actually that of x(ln(x^2-4))/sqrt(x^2-4) , they just forgot the extra 'x'.


P.S. i don't think that the definite integral for ln(x^2-4)/sqrt(x^2-4) between sqrt(5) and sqrt(8) can even be expressed in exact form. (certainly not interms of root extractions or logarithms and exponential values).

 

[FinalFantasy]

LoL.........