Question

Why do we need to check the range of function when doing definite integration?

Answer 1

why is the range of the function checked to see whether it is negative or positive?

Answer 2

Do you mean, for example, when you have: \[\int\limits_{-10}^{2}f(x)dx\] vs
\[\int\limits_{-2}^{10}f(x)dx\]

Answer 3

Or are you referring to when doing substitution?

Answer 4

yes thats what i meant....i dont know why..heard it has something to do with continuity

Answer 5

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?

Answer 6

Well, for example 5, you should know the pieacewise for a function with absolute signs. It's discontinuous, remember?

Answer 7

That is your graph for \(\sf\color{red}{|x|}\)

Answer 8

You have the left side, AND the right side.

Answer 9

The graph for that function is actually:

Answer 10

\(|x|\) isn't discontinuous. I think you mean the graph of its derivative is.

Answer 11

yes. sorry. the derivative is what i meant here. since we are referring to derivativs and anti=derivs.

Answer 12

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

Answer 13

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