perplexus.info :: Calculus : Step Function

Step Function (Posted on 2004-07-07)

A step function f(x) is defined on the interval [0, 1)

From [0, 1/2), the step is 1/2 high.
From [1/2, 3/4), the step is 3/4 high
From [3/4, 7/8), the step is 7/8 high
From [ 1 - 1/(2^k), 1 - 1/(2^(k+1)) ) the step is 1 - 1/(2^(k+1)) high

What is the exact area under the step function?

See The Solution Submitted by Brian Smith

Rating: 5.0000 (1 votes)

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Puzzle Solution

Comment 10 of 10 |

The size above each step in f(x) is always a square.

These are given as: 1/4, , 1/16, .....,, 1/4^n. Their sum is:

(1/4)/(1-1/4) = 1/3

Since the area of the original square is 1, it is established that the area under the step function is equal to : 1-1/3 =2/3

Edited on May 26, 2023, 2:22 am

Posted by K Sengupta on 2023-05-26 02:20:01

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