Question

In this problem, use the general expressions for left and right sums,

left-hand sum=f(t0)Δt+f(t1)Δt+⋯+f(tn−1)Δt
and
right-hand sum=f(t1)Δt+f(t2)Δt+⋯+f(tn)Δt,
and the following table:

t 0 6 12 18 24
f(t) 33 29 28 27 23
A. If we use n=4 subdivisions, fill in the values:
Δt=

t0=
t1=
t2=
t3=
t4=

f(t0)=
f(t1)=
f(t2)=
f(t3)=
f(t4)=

B. Find the left and right sums using n=4
left sum =

right sum =

C. If we use n=2 subdivisions, fill in the values:
Δt=

t0=
t1=
t2=

f(t0)=
f(t1)=
f(t2)=

D. Find the left and right sums using n=2
left sum =

right sum =

Answer 1

Did you graph the data values, and sketch the rectangles?

I don't see what your difficulty is, the question's framework is all laid out for you,
just fill in the values given:

t: 0 6 12 18 24
f(t): 33 29 28 27 23 in a vertical form

for the sum of the 4 "left-sided" f(t) values, start with the first and skip the last
for the sum of the 4 "right-sided" f(t) values, start with the second

for the 2 division part, use
t: 0 12 24
f(t): 33 28 23