Indefinite integral for the square root of a quartic function

  • Thread starter StTheo
  • Start date
  • #1
2
0

Main Question or Discussion Point

I arrived at this problem while trying to find the length of a 3D http://en.wikipedia.org/wiki/Cubic_interpolation" [Broken].

Basically, I'm having to figure out how to integrate ((At4+Bt3+Ct2+Dt+E)1/2)dt

A,B,C,D, and E are constants which have to be plugged in after integration, I'm sorry to say.

All the reduction formulas I've seen use quadratic functions of some kind, so would I have to convert the quartic function into some kind of quadratic function?
 
Last edited by a moderator:

Answers and Replies

  • #2
Char. Limit
Gold Member
1,204
13
In general, it cannot be done simply, I believe. From what I can tell using Wolfram-Alpha, the integral involves the inverse sine function as well as the elliptic integrals of the first AND third kinds. It can't evaluate the integral, though: here.
 
  • #3
2
0
Grr, oh well. However, I hadn't seen that wonderful site you linked to before. I'll probably waste quite a bit of time on it.
 

Related Threads for: Indefinite integral for the square root of a quartic function

Replies
1
Views
6K
Replies
2
Views
3K
Replies
6
Views
13K
  • Last Post
Replies
4
Views
1K
Replies
18
Views
3K
Replies
1
Views
4K
Replies
6
Views
1K
  • Last Post
2
Replies
36
Views
61K
Top