perplexus.info :: Calculus : 100 times a Sawtooth Integral

100 times a Sawtooth Integral (Posted on 2023-12-18)

Evaluate:

   100
100*∫e^x-[x] dx
    0

** [x] is the floor of x, which is equal to the greatest integer greater than or equal to x.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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solution

| Comment 1 of 3

As x increases from 0 to 100, the expression (x-[x]) repeats the same values from 0 to 1, 100 times.

Furthermore, between 0 and 1, [x]=0 and so (x-[x]) = x

100

100*∫e^(x-[x]) dx =

100*100*∫e^x dx = 10000 * (e-1)

Approx 17182.818...

Edited on December 18, 2023, 8:40 am

Posted by Larry on 2023-12-18 08:39:48

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