Can't Find My Mistake. Area between Function and its Floor Function.

Greetings everyone. For the following problem, I think I got the idea but I cannot find the mistake that I made. I know there is one because my answer is which is NOT

. I am also trying to get this right before I sum each representative area between function and the floor function.

Thank you everyone.

http://i45.tinypic.com/v58jz8.png

**My work**

Re: Can't Find My Mistake. Area between Function and its Floor Function.

You should take interval (k,k+1) because you end up with summing up for k=1 to n-1.

If you take interval (k-1,k) then for k=1 this is interval (0,1) but you need to find integral from 1 to n, not from 0 to n.

So, take interval (k,k+1).

Also notice that your answer is .

This is because you chose starting point to be 0, not 1.

Value of integral (using your formula) on interval (1-1=0,1) is , on interval (2-1=1,2) is which is exactly same answer for interval (1,1+1) using required formula.

It is just a question of shifting.

Re: Can't Find My Mistake. Area between Function and its Floor Function.

A really simple solution is just to evaluate

Note that for the summation, i ranges from 1 to n-1 (because we are dealing with floor values).

.

To evaluate we split it up to

and take it on from there.

Re: Can't Find My Mistake. Area between Function and its Floor Function.

Thank youv ery much! I got it!