just tedious work ....
I suggest you make a sketch,
and plot the points (0,20) , (2,22), ....
you will get trapezoids by joining all the y-values and drawing in all the verticals
look at the first trapezoid, its base = 2
the left vertical is 20 and the right vertical is 22
area = 2*(20+22)/2 = 42
second trap
area = 2(22+35)/2 = 57
etc
add them up
for right-bound rectangles, take the height of the right-hand side, and the base will be 2 for all of them
1st rectangle = 2(22) = 44
2nd rectange = 2(35) = 70
etc
I don't know how you were taught the method for midpoint rectangles. Look in your text or your classroom notes
I am in a car and travel for 12 minutes. Below are the speeds in mph, recorded every two minutes. Use trapezoids, right-bound rectangles, and midpoint rectangles to estimate the distance I traveled.
Min 0 2 4 6 8 10 12
Speed 20 22 35 46 50 50 20
Trapezoids:
Right-bound rectangles:
Midpoint rectangles:
I'm confused with the units and midpoint rectangles mostly.
2 answers
For midpoint rectangles my notes say something about expanding the interval but I'm not sure how that works.. And if it's minutes and hours would I have to do something to change it?