This Guy is Mathematician par excellence for all learners.Master of chalk and talk, respecting traditinal values of teacher and the taught rare example of fleeting era.
Hubiera apostado la vida a que la integral no convergía, por el parecido de su gráfica con la gráfica de 1/x. Pero no, me equivoqué y efectivamente converge a √6/2•π Gracias por el ejercicio.
Hello there, great video as always. just a small mistake that didnt impact the answer. On the one before last blackboard I* = sqrt(6) [ lim t->0+ [missing - here] tan-1 sqrt(t/6) + lim t-> inf tan-1 sqrt(t/6)] sinc lim t->0 tan-1 0 is 0 it doesnt matter if it is + or - but still. Also missing a * on the very last line but that is insignificant.
I notice that the integrand 3/[(√x)(x+6)] has no roots in the ℝ domain. So the integral is indeed the area under the curve. You did not mention areas so not an issue here; but if it were the area you were calculating then you would need to check for roots first. (A lot of students forget to do this and just blindly assume the definite integral of a function is equal its area). 😁
@@alifiras1130 Ok the integral of the _pf_ form as shown is ∫1/2√x .dx - ∫√x/(2 (x + 6)) .dx = [√x] -[√x - √(6) tan^(-1)(√x/√6)] = √(6) tan^(-1)(√x/√6) then you take _ℓim_ t ->0 part from the _ℓim_ t ->∞ part as in the end of the video to get your answer.
