The area of a trapezoidis , where and are the lengthsof the parallelsidesand
is the height.In our trapezoidsthe heightis and and are the valuesof the function.Thereforein
findingthe areasof the trapezoidswe actuallyaveragethe left and right endpointsof eachsub-interval.
Thereforea typicaltrapezoidwouldhavethe area
To approximate with of thesetrapezoids,we have
Example1:
Use the TrapezoidalRule to approximate with.
Solution:
We find