definite integral

Integrate 2[x] between 3 - 6

there why do we have split the range ???

Why do we not do this for other functions in general.. like sinx or cosx or any other function?

When do we split the range...

anyone with a good explanation?

3 Answers

62
Lokesh Verma ·

Well this has to do with the continuity of functions.

When we apply integral in an integral, we cannot use the limit directly if there are points of discontinuities in between the points!!

Like we cant integrate tan x between 0 to 2pi. (This is because tanx becomes undefined.. and more importantly discontinuous.)

So we have to take the intervales in (0,pi/2) , (pi/2, 3/2pi) and so on..

This same spirit is in the greatest integer Function!

62
Lokesh Verma ·

@ Challenger: Did u understand why I am trying to say? or not yet!

1
challenger ·

yup i got thank you.............

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