Newton & Riemann integral

  • Thread starter pivoxa15
  • Start date
  • #1
2,255
1
What is the difference between the two? Does the newton integral arise from the fundalmental theorem of calculus and the Riemann integral is the Newton integral but more rigorously defined?
 

Answers and Replies

  • #2
mathwonk
Science Advisor
Homework Helper
2020 Award
11,092
1,292
briefly the newton integral seems to be defined as one side of the second FTC and the riemann integral is the other side, so the FTC seems to say the two definitions of integral agree.
 
  • #3
2,255
1
That seems to make sense. The newton integral is like a black box but really the proper one is the Riemann integral.
 
  • #4
mathwonk
Science Advisor
Homework Helper
2020 Award
11,092
1,292
and it is haeder to define. suppsoe f is any function, and i want to define its enwton integral. i havre tot ell you how to recognize a function G such thast the integral of f is G(b) - G(a).

the right answer, if is only riemNN integrable, and not necessarily continuous, is that G is any liposchitz continuous function whosae derivative exists and equals f almost everywhere.

but how do yopum find such a G? and if you cannot find one, how do you approximate the integral?

seems hopeless without the limit of riemann sums definition.
 

Related Threads on Newton & Riemann integral

  • Last Post
Replies
13
Views
3K
  • Last Post
Replies
19
Views
7K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
8
Views
3K
  • Last Post
2
Replies
28
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
2
Views
2K
Replies
30
Views
8K
  • Last Post
Replies
1
Views
2K
Top