# Question:Getting a weird result with integration of an absolute value

## Question:Getting a weird result with integration of an absolute value

Maple 15

I'm working on a simple toy model as an introductory example to some work I am writing up. I was hoping the example would be simple enough to get some nice analytical results to write up. However, maple is giving me some odd results.

Essentially I have taken the integral of the absolute value of an error that I have caluclated which has given me a somewhat nonsensical result. The attached file contains the specifics (hopefuly it's visible)...

 (1)

Now I have an expression for the absolute error at a given time between an approximate and exact value of a curve - I want to integrate this expression to give a total error value. Doing so the obvious way gives the unexpectedly nice result:

 (2)

This seems odd due to the fact that setting  would give zero total error. I checked this with values   which gives the following results

The plot of the two curves (exact and symbolic) we are determining the error of:

The plot of the absolute value of the time dependent error:

The plot of the area under the curve of the previous plot:

Finally the actual values of the integration for this case:

 (3)

Clearly this does not give 0 total error, but rather a total error of 5. As far as I can tell, setting   does minimise the error (for a fixed ), but it does not make it equal to 0. Any advice on what I've done wrong would be gladly recieved.