Math 142
Section 6.3 Examples
Example 1: An object has velocity v(t) = t2 where t is in seconds and v is in feet per second.
Find an estimate on the distance the object travels from start to 1 second. Use 5 sub intervals and
the right hand endpoints.
Step 1: Divide the interval into equal subintervals.
Step 2: Evaluate the function at the right hand endpoints of the intervals
Step 3: Add up the area of the rectangles.
Math 142
Section 6.3 Examples
Example 2: v(t) is a strictly increasing function. Use the table of values below to answer the
following questions:
t
0 2
4
6
8
10
12
v(t) 0 5.7 9.2 14.1 17.5 19.8 20.2
a) Use 2 equal sub intervals to find an upper and lower estimate of the area under the curve.
b) Use 6 equal sub intervals to find an upper and lower estimate of the area under the curve.
c) Average the two sums from part b) in order to get a better estimate on the area under the curve.