Calc 1 Riemann Sums w/ velocity and distance

[Wm_Davies]

Homework Statement

This is somewhat a repost... except I have figured out some of it and I have cleaned up the question.

Your task is to estimate how far an object traveled during the time interval 0<= t >= 8 , but you only have the following data about the velocity of the object.

[tex]\frac{time (sec)}{velocity (feet/sec)}\frac{0}{4}\frac{1}{1}\frac{2}{-2}\frac{3}{-3}\frac{4}{-4}\frac{5}{-3}\frac{6}{-1}\frac{7}{-3}\frac{8}{-1}[/tex]

"See the attached graph."

(PART 'A') Using the left endpoint Riemann sum, find approximately how far the object traveled. Your answers must include the correct units.

Total displacement = "I have 11ft which is the right answer."

Total distance traveled = "I cannot figure this out"

Homework Equations

Distance = time * velocity
Displacement = time * velocity

The Attempt at a Solution

So I went ahead and got the Riemann sum of the left endpoint on the graph below.

[tex]\Delta[/tex]X = 1

So I just added the y values.

The sum added up to -11 which was the answer for the displacement. I do not know why this is not the answer for the total distance but maybe I am missing something elementary.

 

[computerex]

To find the distance traveled find the area of the shaded region. Area is always positive BTW :D

 

[Wm_Davies]

To find the distance traveled find the area of the shaded region. Area is always positive BTW :D

I tried to compute the area, but I am not getting it. Also area if area is always positive then why would the area of a curve under the x-axis be negative?

 

[computerex]

I tried to compute the area, but I am not getting it. Also area if area is always positive then why would the area of a curve under the x-axis be negative?

Distance can never be negative.

 

[Wm_Davies]

Distance can never be negative.

O.k. that actually makes tons of sense (I figured I was making some elementary mistake). So, I added up the areas as positive numbers and everything was correct. Thanks for the help.