Integration

[dan_bo]

Not sneering 26, just a maths wimp engineer/ technician.

I work in a rich field of optical physics, microelectronics and applied chemistry, I just leave the maffs to the brains.....I've done OK lasting more than a decade without having to rely on it myself.

 

[twentysix by twentyfive]

Not sneering 26, just a maths wimp engineer/ technician.

I work in a rich field of optical physics, microelectronics and applied chemistry, I just leave the maffs to the brains.....I've done OK lasting more than a decade without having to rely on it myself.

Sorry dan. I'm glad you are techy enough to appreciate maffs. I can't say I'm a maffs man either really but I have had my moments and couldn't have been useful in my career without it.

Now don't wimp - it's just practice. Have a play with what you can. You won't be hung drawn and quartered if you can't do String Theory.

 

[marinyork]

Ah right indeed. So the answer is Imaginary and the real integral is Zero.

Thanks for all that.

NP. FWIW I think it might be a typo, but as it's such a bread and butter example in complex analysis this seemed easier than any other method. Funnily enough there are quite a few other integrals where you could prove that over that range that real integral is zero, but that's the easiest one. To be able to get what mathematica gets in terms of polylogs on a paper calculation needs a lot of fiddling with special functions which is not that easy. I suppose you could just look at the real integrals in the range [0,1] and [1,∞) from mathematica and say they cancel out, makes a nice presentation I suppose.

I take the point about it being a first year undergraduate course, but someone later on in their studies would be expected to employ all kinds of tricks whether it be partial fractions, integration by parts, substitution, series or a convergence test or more likely numerical analysis.

 

[longers]

I use trig. every day at work!

If I did I might not have had to draw it out on squared paper

I'm making one of these. My maths is good enough to know that £7.22 for the timber means I'm making a bit of a saving.

 

[marinyork]

Out of interest, what would that sort of maths be used for?

I've been trying to get my head round simple trigonometry today for the first time in a while so am just curious.

Might not be what you wanted but slightly higher up they are linked to trigonometry.

Integrate sin(x) and you get -cos(x) plus a constant. Integrate cos(x) and get sin(x) plus a constant.

Complex numbers and trig are related too e[sup]iθ[/sup] = cos(θ) + isin(θ)

and even (cosx + isinx)[sup]n[/sup] = cos(nx) + isin(nx) for integers n which leads to being able to calculate things like sin(2x), sin(3x) and so on.

Take quadratic equations and how to sort them out with this made famous at secondary schools

x= (-b ± √(b[sup]2[/sup] -4ac))/ (2a)

This is to solve equations like 3x[sup]2[/sup] + 2x +1=0

{-2 ± √(2[sup]2[/sup] -4*3*1) }/ (2*3)

= -2 ± √(4-12) all divided by 6.
-1/3 ±(√-8)/6
=-1/3 ±1/3√-2 but what is the square root of -2?
For anything where b[sup]2[/sup] ≥ 4ac we get an answer with real numbers. Where b[sup]2[/sup] < 4ac we run into problems and we don't get a solution that makes any sense with real numbers.

 

[threebikesmcginty]

If I did I might not have had to draw it out on squared paper

I'm making one of these. My maths is good enough to know that £7.22 for the timber means I'm making a bit of a saving.

You can have my SMP book of Elementary Tables if you want, longers. Helps you to understand what's going on before you put all your trust in the scientific calculator.