Three integrals I can't solve

  • Thread starter Dustinsfl
  • Start date
  • #1
699
5
j=[tex]\int\sqrt{1-x^{4}}[/tex]

k=[tex]\int\sqrt{1+x^{4}}[/tex]

l=[tex]\int\sqrt{1-x^{8}}[/tex]

I am trying to figure out the order for example j<k<l. I don't know how to integrate any of these.
 

Answers and Replies

  • #2
699
5
I forgot to mention 0 to 1 are the bounds of all 3.
 
  • #3
Dick
Science Advisor
Homework Helper
26,260
619
Don't even try to integrate them. Can't you order the functions you are integrating on [0,1]?
 
  • #4
699
5
I am trying to determine the order but I don't know how to do that without solving them.
 
  • #5
Dick
Science Advisor
Homework Helper
26,260
619
Which is largest, sqrt(1+x^4), sqrt(1-x^4) or sqrt(1-x^8)?
 
  • #6
699
5
+, but for the x to the 8th and 4th it depends on if 0<x<1 or if x is outside that range. If x is between 0-1, the order would be +, 8th power, 4th. If not in that range, +, 4th, and 8th.
 
  • #7
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,470
246
I don't think these are integrable in terms of elementary functions.

But if you just want to sort them from lowest to highest, that shouldn't be too hard.

For example, compare the integrands of j and k:

[tex]\sqrt{1-x^4}[/tex]

and

[tex]\sqrt{1+x^4}[/tex]

Clearly the first one is [itex]\leq[/itex] the second one for all [itex]x \in [0,1][/itex], and the inequality is strict for [itex]x \in (0, 1][/itex], so that implies [itex]j < k[/itex].

Comparing the integrand for L shouldn't be too much harder - give it a try and let us know if you get stuck.
 
  • #8
Dick
Science Advisor
Homework Helper
26,260
619
+, but for the x to the 8th and 4th it depends on if 0<x<1 or if x is outside that range. If x is between 0-1, the order would be +, 8th power, 4th. If not in that range, +, 4th, and 8th.
Didn't you say the range of integration is 0<=x<=1?
 
  • #10
Dick
Science Advisor
Homework Helper
26,260
619
I did.
Hence, why are you worried about values outside that range?
 
  • #11
j=[tex]\int\sqrt{1-x^{4}}[/tex]

k=[tex]\int\sqrt{1+x^{4}}[/tex]

l=[tex]\int\sqrt{1-x^{8}}[/tex]

I am trying to figure out the order for example j<k<l. I don't know how to integrate any of these.
http://www.quickmath.com/
 

Related Threads on Three integrals I can't solve

  • Last Post
Replies
1
Views
1K
  • Last Post
2
Replies
27
Views
3K
Replies
2
Views
8K
  • Last Post
Replies
6
Views
4K
Replies
16
Views
2K
Replies
22
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
19
Views
1K
Replies
4
Views
1K
  • Last Post
Replies
13
Views
2K
Top