Average of a function?

Question

This is the function: http://www.facebook.com/album.php?aid=341&l=46236&id=1462476387

Finding the period and the value at B is easy

T = 4 sec

B = - 3.67V

Finding the average should not be a problem but I have been working on this for an hour and cant get it right for some reason ( probably the part of the graph that lies on the x axis is doing something funny )

Any help is appreciated.

Thank you

Answer 1

To find the average of the function you need tko integrate the function between the beginning and end of one period and divide that by the period legnth. (this is the formula for working out the average of any function beteen two points).

The integral shouldnt be too hard to find as the graph is nicely divided into rectangles and triangles the areas of which are fairly easy to find

Answer 2

Well, to average something, you sample it a lot of times, then divide by the number of samples.  When you do this lots and lots, you get a limit...  Do this sound familiar?  It is just integration!  When you are averaging a function, it is the same as finding the average area.  The area under the 4s period is:

area = 11*1 + 3/2*11/2 - 11/3*1/4

= 55/3

The exact value of the average area is therefore 55/12V, which is the average of the function.