Complex Complexities! (1 Viewer)

[acmilan]

Break from study time:

Firstly, its an improper integral, need limits to evaluate it

Secondly, int du/u = ln|u| + c

 

[who_loves_maths]

firstly, the limits are specified: from x = pi to x = 0.

secondly however, you are correct in your second point
this goes to show the fallacy in the fact that schools (well, at least in mine) do not impose on students the importance of having absolute value signs around 'ln' integrals after doing integration.

the fact is that one does not lose marks in exams if one forgets the absolute value signs, when the reality is that they should be marked wrong for it.

 

[Dumsum]

I remember doing a question in one of my trial exams (forget if it was 3u or 4u) but I did it and kept getting ln(negative). Then I realised this point that absolute value needs to be taken it had be confused for a while though.

 

[who_loves_maths]

^ yes it is a "confusing" aspect of logarithmic integrals. esp. when you take into consideration of the fact that some logarithmic integrals are fine without the absolute values signs, while some other are not and need them to avoid paradox. and to know whether an integral needs them or not, you would need to consider the domain and range of the function... which takes up unnecessary time during, say, exams.

so the problem is best overcome if, for every logarithmic integral, absolute signs are imposed - but this is not always re-inforced in the teaching of integration at teh secondary level.