anonymous
  • anonymous
Why do we need to check the range of function when doing definite integration?
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
why is the range of the function checked to see whether it is negative or positive?
abb0t
  • abb0t
Do you mean, for example, when you have: \[\int\limits_{-10}^{2}f(x)dx\] vs \[\int\limits_{-2}^{10}f(x)dx\]
abb0t
  • abb0t
Or are you referring to when doing substitution?

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anonymous
  • anonymous
yes thats what i meant....i dont know why..heard it has something to do with continuity
anonymous
  • anonymous
example 5 and 6 on this page explains it http://tutorial.math.lamar.edu/Classes/CalcI/ComputingDefiniteIntegrals.aspx But it would be great if i can see a graph visualization or an expounding on this part.......can i have a pointer?
abb0t
  • abb0t
Well, for example 5, you should know the pieacewise for a function with absolute signs. It's discontinuous, remember?
abb0t
  • abb0t
|dw:1378395802473:dw|
abb0t
  • abb0t
That is your graph for \(\sf\color{red}{|x|}\)
abb0t
  • abb0t
You have the left side, AND the right side.
abb0t
  • abb0t
The graph for that function is actually: |dw:1378395956443:dw|
anonymous
  • anonymous
\(|x|\) isn't discontinuous. I think you mean the graph of its derivative is.
abb0t
  • abb0t
yes. sorry. the derivative is what i meant here. since we are referring to derivativs and anti=derivs.
amistre64
  • amistre64
we need to check the range to make sure that the function can be defined at every point with in it. spose we wanted to integrate 1/x from -1 to 3 ? we have an issue at x=0
amistre64
  • amistre64
i spose 1/x might be a bad example graphwise since the interval from -1 to 1 cancels out ... but it still presents the issue of the trouble spots within a range

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