1. ## area

For this , indicate which give(s) an overestimate for the integral

A. RIGHT(n)
B. LEFT(n)
C. TRAP(n)
D. MID(n)

(Click on the graph for a larger version.)

2. Originally Posted by amiv4
For this , indicate which give(s) an overestimate for the integral

A. RIGHT(n)
B. LEFT(n)
C. TRAP(n)
D. MID(n)

(Click on the graph for a larger version.)
did you draw what the rectangles (or trapeziums) would look like for each rule? do you notice any one that would have a larger area than the others?

3. well i thought that the left and right would end up being equal.
then the trapezoid would be an under estimate
and im not sure bout the midpoint

4. Originally Posted by amiv4
well i thought that the left and right would end up being equal.
yes. but would they be overestimates or underestimates?

then the trapezoid would be an under estimate
yes

and im not sure bout the midpoint
if we know that one has to be, then we could pick this one by process of elimination.

if you don't like that, my suggestion is to draw the rectangles for each rule on the same graph, so you can compare them side by side. to see which gives the largest area. of course, it helps to draw a grid over the figure so you can count the units of area. otherwise, come up with an example of a function that looks like this and actually do some estimates for it. use each of the rules to, say, find the area of the function $\displaystyle y = -x^2 + 5x$ between x = 0 and x = 5

5. k i got under estimate for left, right, trapezoid. and then over for middle. right?