HELP! Integration Using Euler's Formula (2 Viewers)

[Carrotsticks]

Define what you mean by "very flawed," I can only see a few "flaws". Also what program did you use?

I used MathType because I was being lazy.

What flaws do you see? List all the ones you can find.

 

[SpiralFlex]

I used MathType because I was being lazy.

What flaws do you see? List all the ones you can find.

First of all, you need brackets around your integrand.

Second, your sum of 1+1/2+1/3+1/4 is not equal to inf? I am puzzled by that.

Third, your constants of integration? (Are they applicable here?)

Also can you actually call out -ln(1-1) as infinity?

Also x<0. But you subbed in zero!

*Adding more*

 

[Carrotsticks]

First of all, you need brackets around your integrand.

Second, your sum of 1+1/2+1/3+1/4 is not equal to inf? I am puzzled by that.

Third, your constants of integration? (Are they applicable here?)

Also can you actually call out -ln(1-1) as infinity?

Also x<0. But you subbed in zero!

*Adding more*

Suppose I took the limit as x-> 0 from the negative side (which should cross off a few of your points)

What other flaws do you see?

 

[SpiralFlex]

I don't see any more, though I will look harder.

 

[kingkong123]

wait, so we should never use methods outside the syllabus? :S

 

[Carrotsticks]

wait, so we should never use methods outside the syllabus? :S

Nope. Besides, the questions are written to be do-able using methods within the Syllabus anyway.

I don't see any more, though I will look harder.

A more 'rigorous' proof would have the following differences:

1. Instead of having an infinite series like this (which can get quite tricky sometimes) then using the limiting sum formula, sum the series up to exp(nx) and then use the sum of GP formula.

2. Integrate both sides with limits (-inf) --> t

3. You will have a 'residual term' or an 'error term', which can be defined as E(t) that you have to show approaches 0 as n --> inf

4. I also interchanged the limit operation and the summation operation, which must be justified. (In this case it works, but not always)

I'm not saying that you need to learn this.

The point that I am trying to make is regarding your teacher's comments about being 'Mathematically Correct'.

Like I said, most students will not be able to tell, and will often fudge something in the attempt to acquire the result of the question.

 

[largarithmic]

I'm pretty sure you can get away with some not "mathematically correct" things at school... like full analytical rigour is not really part of the course, and I'm not convinced every marker would pick really subtle things up either.

 

[cutemouse]

Do you just treat i as a constant or something?

Yes you can treat 'i' as a constant when doing integration.

Another interesting point is that the complex exponential function e^(i theta) is periodic with period 2*pi*i. This makes the complex log function a bit more complicated.

 

[seanieg89]

Yes you can treat 'i' as a constant when doing integration.

Another interesting point is that the complex exponential function e^(i theta) is periodic with period 2*pi*i. This makes the complex log function a bit more complicated.

The period is just 2pi.

 

[cutemouse]

The period is just 2pi.

Hmm... Are you sure?

...

 

[seanieg89]

Yes you can treat 'i' as a constant when doing integration.

Another interesting point is that the complex exponential function e^(i theta) is periodic with period 2*pi*i. This makes the complex log function a bit more complicated.

The function you wrote down was e^{i*theta}

 

[cutemouse]

The function you wrote down was e^{i*theta}

whoops my bad -- I meant the complex exponential function.

 

[seanieg89]

Figured .