Consider the four functions shown below. On the first two, an approximation for $\int_a^b\,f(x)\,dx$ 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 $n=2$ subdivisions using the midpoint rule.
Is this method an over- or underestimate?

4. On a copy of graph number 4, sketch an estimate with $n=2$ subdivisions using the trapezoid rule.
Is this method an over- or underestimate?