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better yet, let me convince you what is the physical representation of the integral from x=a to x=b ?
i don't know much about integrals but i know they represent sum of anything so how could we sum up zero
that is one convincing argument^
There is nothing like integral of zero.You should mention with respect to which you are integrating it.If it is the integration of 0 with respect to ,say some dt,then its value is a constant.in the case of integral of zero with anything gives us a constant.
the integral of zero is asking about the area under the curve f(x)=0 what is the area under the line y=0 ?
@TuringTest is it ...lol..i am in 9th grade..but love sign of integral lol
Well your explanation is quite valid :) As I side note, I always loved the symbol of the integral as well ;)
:) thanks :)
@honey26 your explanation is not right, you are describing the integral of 1
the integral of zero has a meaning: the area under the curve of y=0, or the sum of all the y values in some interval as @erica.d said, which is 0+0+0+0+0....=0 so there are two ways to see that the answer is zero
sorry, what I said is only for definite integrals, I think I see your point now @honey26
yah,it is true that integral of zero means area under the line y=0 but indefinite integral of 1 with respect to dt gives us t but not a constant,right.
does indefinite integral represent sum @TuringTest i guess No :)
yes it does represent a sum actually the symbol you love so much \[\int\]is in fact a medieval S that stands for "summa"
oh thanks for this nugget of wisdom ..... :D
indefinite integral is also a sum but it has no limits like definite integral.
guys i need to learn it more ::( i feel so stupid here
...and that is why the indefinite integral of 0 can be a constant, because \[\int0dx\]asks "what function is 0 the derivative of?" the answer is any constant, (or in multivarible terms, any variable that does not depend on x)
if you are in 9th grade @erica.d you are way ahead of where I was back then. I was busy failing algebra, I had to go to summer school ;)
he he thanks :) i am just curious to solve those complex equation that i have seen on TV
you will, I'm sure :D