What does the integral represent?

  • Thread starter Thread starter Manni
  • Start date Start date
  • Tags Tags
    Integral
Click For Summary
The integral of R(t), which represents the rate of volume per unit time, signifies the total volume change over a specified time interval. Initially, there was uncertainty about whether it simply represented total volume, but the clarification helped refine the understanding. The term "total volume change" is more accurate and aligns better with the concept being discussed. This distinction resolved the confusion regarding the definition. Overall, the integral effectively captures the cumulative effect of the rate over time.
Manni
Messages
42
Reaction score
0
Hey guys I was trying to think conceptually and got a little lost. If R(t) represents the rate of volume per unit time what would it's integral represent?

My initial guess was that it represents the total volume over that interval of time but it feels incomplete, or even wrong.

Help?
 
Physics news on Phys.org
Try saying "total volume change" instead of just "total volume". Does it feel better now?
 
Yup, I don't know why I was questioning my definition so much. Thanks Dick :)
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

What does the area under a volume vs time graph represent?
  • · Replies 8 ·
Replies
8
Views
4K
Drawing a Graph using Integral Equation
  • · Replies 11 ·
Replies
11
Views
2K
Turning a real world problem into a calculus problem
  • · Replies 18 ·
Replies
18
Views
3K
High School What does the Minkowski spacetime interval represent and how is it determined?
  • · Replies 20 ·
Replies
20
Views
2K
Question about Vector Fields and Line Integrals
  • · Replies 5 ·
Replies
5
Views
2K
Calculating crossproduct integral, Parametrization
  • · Replies 5 ·
Replies
5
Views
2K
Power dissipated over 1 cycle of a AC source-free RLC series circuit?
  • · Replies 6 ·
Replies
6
Views
904
Show Regular Homotopy thru curve and its arclength parameters
  • · Replies 1 ·
Replies
1
Views
1K
Rate of change and integrating factor
  • · Replies 2 ·
Replies
2
Views
2K
Verifying the flux transport theorem
  • · Replies 4 ·
Replies
4
Views
2K