cal. (1 Viewer)

[spikestar]

Hi, can some 1 plz tell me how do i find the anti-diff of y=Ln(x)

 

[housemouse]

Integration by parts??????

 

[spikestar]

yes, !

 

[STx]

well done...

 

[Mountain.Dew]

using integration by parts...

this will get u started...make v' = 1, u = lnx.

go from there

 

[hyparzero]

surely you can use the Machurin Series, much more practical and confuses the teacher?

 

[Slidey]

Um... I think you mean Mclaurin. And unless you plan to write up a detailed explanation for the other users of this forum, it'd be best to leave Mclaurin series out of this.

Risking marks in exams is entirely your onus.

 

[hyparzero]

whoops, i meant Maclaurin Series

Explanation
A Maclaurin series is a Taylor series expansion of f(x) about 0, also known as a power series.

It is primarly used to approximately integrate transcendal functions such as e^x2

f(x) = f(0) + f'(0)x + f''(0)x² /2! + f'''(0)x³ /3! + f⁽⁴⁾(0)x⁴ /4! + f⁽⁵⁾(0)x⁵ /5! + ............ and so on to infinity

 

[buchanan]

Yeah. But it's got a Taylor's series:

<table align="center" width="100%" cellpadding="0" cellspacing="0" style="padding-left: 50px" border="0"><tr style=""><td align="right" width="1"><img src="http://mathworld.wolfram.com/images/equations/TaylorSeries/inline22.gif" width="26" height="18" alt="lnx" /></td><td align="center" width="14"><img src="http://mathworld.wolfram.com/images/equations/TaylorSeries/inline23.gif" width="14" height="18" alt="=" /></td><td align="left"><img src="http://mathworld.wolfram.com/images/equations/TaylorSeries/inline24.gif" width="238" height="37" alt="lna+(x-a)/a-((x-a)^2)/(2a^2)+((x-a)^3)/(3a^3)-..." /></td></tr></table>

As for the integral of lnx, it's xlnx-x+c using Mountain.Dew's method.

You could do it without Taylor's series

&int;lnxdx=&int;lnx(dx/dx)dx
=xlnx-&int;x(dlnx/dx)dx
=xlnx-&int;x(1/x)dx
=xlnx-&int;dx
=xlnx-x+c

Note that Taylor's series wasn't first discovered by Taylor. It was attributed to Brook Taylor who published it in 1715 in Methodus in crementorum directa et inversa. But James Gregory wrote it on the back of a letter from a bookseller on January 30, 1671 (preserved in the library of the University of St. Andrews).

Taylor:

Gregory:

Maclaurin:

 

[hyparzero]

Slight problem: the "MacLaurin series" of ln(x) doesn't exist - try deriving it.

instead of using fⁿ(0), use fⁿ(1)
and replace all xⁿ with (x-1)ⁿ

 

[Yip]

as u said before hyparzero, maclaurin series are about 0, not 1

 

[hyparzero]

as u said before hyparzero, maclaurin series are about 0, not 1

Taylor

 

[Roobs]

hmmm.....ill stick to parts, appease the board and then men upstairs, n then figure out nifty methods later......

the hsc is bad enough without trying to do things in a manner more complicated than required

 

[Rax]

hmmm.....ill stick to parts, appease the board and then men upstairs, n then figure out nifty methods later......

the hsc is bad enough without trying to do things in a manner more complicated than required

Amen to that. All this serious stuff is messin with me already.

On a Side Note, Hello Roobs. I belive I saw you at the Maths Extension II day by Mark Arnold in Lismore.
And thats about it.

GG