Question

the velocity v(t) in the table below is increasing for 0≤t≤12.

t 0 3 6 9 12
v(t) 26 27 30 35 40

A. Find an upper estimate for the total distance traveled using
n=4 subdivisions: distance traveled =
n=2 subdivisions: distance traveled =

Find a lower estimate for the total distance traveled using n=4.
distance traveled =

Answer 1

so..i have no clue what goingon. did any work on this yet?

Answer 2

i suggest plotting the points

notice that v(t) is increasing so use rectangles where the right corner touches the graph you will get an overestimate (upper estimate) and if you use left sided rectangles you get a lower estimate.

Answer 3

so for example, if you want an upper estimate with n = 4 rectangles then:

each rectangle would have a base of 3
and each height would be the value of the function at the right end point

so your estimate would be 3(27 + 30 + 35 + 40)



sorry for bad artwork but this is kind of what you want to get at