perplexus.info :: Calculus : One, Two, Three, Floor Integral

One, Two, Three, Floor Integral (Posted on 2007-11-12)

Evaluate:

  ₄
∫ [t + [t + [t]]] dt
 ^-4

where [p] is the greatest integer ≤ p.

See The Solution Submitted by K Sengupta

Rating: 4.0000 (1 votes)

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Step by Step Solution

Comment 1 of 1

Am I missing something?

It looks like [t + [t + [t]]] is just 3*[t]

This is a step function that is
   0 between 0 and 1,
       3 between 1 and 2,
   6 between 2 and 3,
   9 between 3 and 4.

Between -4 and 0 the steps are -12, -9, -6, -3.

The integral is the sum of these 8 steps, which is -12.

Posted by Steve Herman on 2007-11-12 18:14:03

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