perplexus.info :: Calculus : Floor on an Exponential Integral

Floor on an Exponential Integral (Posted on 2025-03-12)

Evaluate the integral

2
∫ Floor(e^x) dx
0

No Solution Yet Submitted by Brian Smith

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solution

| Comment 1 of 5

From examination of the graph of floor(e^x), the definite integral sought is:

ln(2)

+2*(ln(3)-ln(2))

+3*(ln(4)-ln(3))

+4*(ln(5)-ln(4))

+5*(ln(6)-ln(5))

+6*(ln(7)-ln(6))

+7*(2-ln(7))

the coefficients being the heights of the steps and the natural logs being where the transitions in the floor values take place.

Its evaluation is approximately 5.47483863893459....

Of course ln(3)-ln(2) can be written as ln(3/2), etc.

Posted by Charlie on 2025-03-12 09:01:45

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