Consider the four functions shown below. On the first two, an approximation for is shown.

1.2.
3.4.

(Click on any graph to get a larger version.)

1. For graph number 1, Which integration method is shown?




Is this method an over- or underestimate?


2. For graph number 2, Which integration method is shown?




Is this method an over- or underestimate?


3. On a copy of graph number 3, sketch an estimate with subdivisions using the midpoint rule.
Is this method an over- or underestimate?


4. On a copy of graph number 4, sketch an estimate with subdivisions using the trapezoid rule.
Is this method an over- or underestimate?