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Find following integration

$\int_{a}^{b}\ [x] dx + \int_{a}^{b}\ [-x] dx $ where [.] denotes greatest integer function

kalpeshmpopat
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  • Time to draw a picture. – Ragib Zaman Mar 30 '13 at 07:55
  • but please also not to use empirical words.like Find.simple please help me to find it or like this – dato datuashvili Mar 30 '13 at 07:56
  • Instead of continuing to rapidly fire questions without any kind of motivation or personal thoughts, you might want to slow down the pace and to add this kind of input to your future questions. In the present case, it is clear that you did not spend one minute to think about the question you were asking. – Did Apr 01 '13 at 08:31
  • This is Section 1.15 Exercise 3 from Apostol's Calculus pg. 70 – j.d. allen Jan 06 '16 at 19:36

1 Answers1

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Note that if $x$ is not an integer, then $\lfloor x \rfloor +\lfloor -x\rfloor=-1$. And the integral is not affected by function values at finitely many points. So the integral is $-(b-a)$.

André Nicolas
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