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?

when we plot out the function graphically we can find the area by integrating the different functions of 'x' at different intervals the answer is obtained to be 43/64= .546875 .

area = ∑ 1/2dx in the interval [0,1/2) +
∑ 3/4dx in the interval [1/2,3/4) +
∑ 7/8dx in the interval [3/4,7/8) +
∑ 1dx in the interval [7/8,1)

= 43/64

Posted by sudip on 2004-07-08 00:28:51