For define a step function on the interval by

Then, define

- Calculate .
- Find all values of such that .

- We calculuate:
- .

* Note: There is an error in the book. The answers in the back of the book claim that , which is incorrect. *

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#
Stumbling Robot

A Fraction of a Dot
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Calculate the values of an integral of a step function

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4 comments

### Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):

For define a step function on the interval by

Then, define

- Calculate .
- Find all values of such that .

- We calculuate:
- .

* Note: There is an error in the book. The answers in the back of the book claim that , which is incorrect. *

Hi Rori. Can you please elaborate further about your solution in part b please?

You can solve it pretty fast just by a little inspection, you can see pretty fast for witch value of p, the sum -1 + 2 -3 + …… + s(p-1) = 7 (absolute value)

You can split the sum in even and odd part and then it is easy to have a closed formula.

From the integrals you can observe that this formula follows a recursive pattern, which is . Then you can code this function in your favourite programming language and enter a while loop to find out for which ‘s you get or .