Can I do that in calculus? (canceling the dt terms in the numerator and denominator)

  • #1
NODARman
54
13
TL;DR Summary
.
Hi, just wondering if that's possible in calculus.
(See the attachment)
 

Attachments

  • 166920054969935055318737542524.jpg
    166920054969935055318737542524.jpg
    37.6 KB · Views: 16

Answers and Replies

  • #2
topsquark
Science Advisor
Insights Author
Gold Member
MHB
1,804
741
TL;DR Summary: .

Hi, just wondering if that's possible in calculus.
(See the attachment)
What you wrote was essentially correct. But...

In reality? No. The derivative notation ##\dfrac{d \theta }{dt}## is not actually a fraction so you cannot cancel the dt's.

However, in practice you can "cancel" the dt's. It's a similar effect to the chain rule: ##\dfrac{d \theta }{dx} = \dfrac{d \theta }{dt} \cdot \dfrac{dt}{dx}##. Again, there is no real cancellation, but it appears that way.

Mathematicians in the 1800s spent a great deal of time showing how you can treat a differential element as a fraction. Most of the time you can get away with it.

-Dan
 
  • Like
Likes DaveE, vela and NODARman
  • #3
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2022 Award
23,784
15,399
Technically the bounds on the integral need to change to ##\int_{t(0)}^{t(2\pi)}## if you are integrating wrt ##t##.
 
  • Like
Likes DaveE and topsquark

Suggested for: Can I do that in calculus? (canceling the dt terms in the numerator and denominator)

  • Last Post
Replies
3
Views
580
Replies
5
Views
113
Replies
15
Views
1K
  • Last Post
Replies
9
Views
976
Replies
15
Views
695
Replies
11
Views
988
  • Last Post
Replies
3
Views
2K
Replies
9
Views
669
Replies
13
Views
220
  • Last Post
Replies
3
Views
479
Top