Variety of Calculus questions

t (s)	0	12	24	36	48	60
v (ft/s)	32	28	24	22	24	28

Readings at 12 second intervals. Estimate distance traveled Deltax= 12

1. estimate distance using the velocities in the beginning of the time intervals:

=156 = 12(28+24+22+24+0)=L6 This is correct



2. give another estimate at the end of the time intervals.

I did 12(32+28+24+22+24+28) = 1896 =R6 Which is wrong


PART B)

Are your estimates in parts (a) and (b) upper and lower estimates? Explain.
a (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.
b (a) is a lower estimate and (b) is an upper estimate since v is an increasing function of t.
c. (a) and (b) are neither lower nor upper estimates since v is neither an increasing nor decreasing function of t

I chose b but it's wrong. But I believe it is choice c since the intervals are an irregular curve

Hey Steelers72.

I am also inclined to go with c) as well for the answer.

Yes, (c) is correct: v decreases from 24 to 36 and increases from 36 to 48.

For the first part of the problem, I get:
using velocity at beginning of interval: 12(32+28+24+22+24) = 1560
using velocity at end of interval: 12(28+24+22+24+28) = 1512

- Hollywood

Thank you for your replies! Im confused with the end of interval. Why would 32 not be included? I was thinking not to include the 60s and 28 ft/s since it's at the end(?) You're right, but could you explain why 32 is left out? thanks again!!

Oh wow, never mind! I answered my own question.

For left hand sums, you leave out the right-most measurement and for right hand sums you leave out the left-most measurement right?

That's correct.

- Hollywood