- Consider the function on the interval
[-1,3]. Use the command
`leftsum`to approximate the definite integralto two decimal places. Then explain why the

`leftsum`and`rightsum`commands give the same numerical values for the same number of subintervals. (Hint - use the`leftbox`and`rightbox`commands to see what is going on.) - Suppose that the velocity of a particle moving in one dimension
is given by
Find the average value of

*v*(*t*) on the following time intervals.- a.
**[0,5]** - b.
**[0,10]** - c.
**[5,10]**

- a.
- Let the continuous function
*v*(*t*) represent the velocity of a particle moving in one dimension. Let*a*and*b*be real numbers in the domain of*v*and let*c*be (*a*+*b*)/2. That is,*c*is exactly halfway between*a*and*b*. Show that the following equation is always satisfiedwhere is the average value of

*v*on the interval [*a*,*b*], is the average value of*v*on the interval [*a*,*c*], and is the average value of*v*on the interval [*c*.*b*]. Note - this is not a Maple problem. This problem is a thinking problem. I would suggest leaving some space on your worksheet and writing your answer in by hand. Part of using Maple is learning when not to use it.

Fri Jan 24 15:07:34 EST 1997