Integration

[asterix]

Sounds like the kind of stuff that would be discussed at the world's most boring dinner party.

To which you we appear to have been invited..

 

[rich p]

Incidentally, when I'm watching University Challenge the answer is either, 0, 1 or the square root of -1.

If this doesn't help, I'm all out of ideas.

 

[darth vadar]

He's got you bang to rights Darth. I'll say no more

He is.

Just off to get my Prozac sandwich for breakfast before being returned to my padded cell.

Eeek!!!!

 

[Aperitif]

Something doesn't quite add up here...Dan posts once and it is multiplied by four and Rich is a =1= 4/3 pies are too much - even for Vernon!

 

[byegad]

Sounds like the kind of stuff that would be discussed at the world's most boring dinner party.

You wouldn't say that if it was your x being Integrated!

 

[MacB]

Boring? - No, Bloody difficult to understand - Yes - but I could be applying that to Teefs puntastic posts as well

 

[Aperitif]

Boring? - No, Bloody difficult to understand - Yes - but I could be applying that to my bicycle parts and frame combination / speculation posts as well

I understand Al - and suitable fixed for you!

 

[MacB]

I understand Al - and suitable fixed for you!

Yeah, you're cards marked big fella, Marin's going to be doing some trajectory and impact calculations for me, just right for taking down a large person!

 

[threebikesmcginty]

Yeah, you're cards marked big fella, Marin's going to be doing some trajectory and impact calculations for me, just right for taking down a large person!

MacB Vs Teef - it'll be like the Goliath and Goliath Bible story.

 

[Aperitif]

Yeah, you're cards marked big fella, Marin's going to be doing some trajectory and impact calculations for me, just right for taking down a large person!

Oh - you're actually riding them these days are you Al?

 

[rich p]

Something doesn't quite add up here...Dan posts once and it is multiplied by four and Rich is a =1= 4/3 pies are too much - even for Vernon!

I slept like a log last night and woke up inthegrate.

 

[Aperitif]

I slept like a log last night and woke up inthegrate.

Just a hint of flaming there Rich...be careful, or I'll get Al to spread sheet on you...

 

[twentysix by twentyfive]

fook i used to be able to do these in my sleep

about 23yrs ago

In fact I`ve just been reaquanting myself with trigonometry since my wife started her Uni course!


(d ((Log[1 - I x] + Log[1 + I x]) Log[x] + PolyLog[2, -I x] + PolyLog[2, I x])) / 2

Sorry all - been elsewhere since I posted.

Err - Yes. I got that too from Mathematica. But it's from an undergraduate science course and I'm pretty sure PolyLogs are not in the syllabus.

 

[Aperitif]

Sorry all - been elsewhere since I posted.

Err - Yes. I got that too from Mathematica. But it's from an undergraduate science course and I'm pretty sure PolyLogs are not in the syllabus.

Don't worry 650 - you haven't missed anything interesting...

 

[twentysix by twentyfive]

D'oh. An easier substitution is z=x. Residue theorem. Integrate around the simple pole z=i. If you can't do it I'll write something up later.

Just use the principal logarithm value ln(i) = πi/2. Use some contour that makes sense and doesn't muck it up. Set all bits of this equal to the value from the residue theorem. Strip out whichever bit you want. Take real/imaginary parts as as radius → ∞. As there is no real part in whatever it is you have constructed then the answer is obviously zero!

Ah ha marinyork. It has been a very very long time since I've done contour Integration. I'll give that a go. As said above the question is from an undergrad 1st year science course. 1st term too. So I'm not sure they have covered contour integration yet. I shall check.

The lead into the question was show Integral(0->Infinity) Ln[x]/x^2 dx = -Integral (0->1) Ln du which is easy with a substitution of u=1/x. So I wondered if the question was a typo for Ln[x]/(1+x)^2 dx. That one drops out as Zero (the proof asked for) easily using u=1/(1+x). However I've been told I must not alter the question........... I still think that I'm correct about the typo tho'.

So I'm off to brush up on contours.