- #1

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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.

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- Thread starter Dustinsfl
- Start date

- #1

- 699

- 5

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.

- #2

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- 5

I forgot to mention 0 to 1 are the bounds of all 3.

- #3

Dick

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Don't even try to integrate them. Can't you order the functions you are integrating on [0,1]?

- #4

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I am trying to determine the order but I don't know how to do that without solving them.

- #5

Dick

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Which is largest, sqrt(1+x^4), sqrt(1-x^4) or sqrt(1-x^8)?

- #6

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- #7

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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

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Didn't you say the range of integration is 0<=x<=1?

- #9

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I did.

- #10

Dick

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I did.

Hence, why are you worried about values outside that range?

- #11

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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/

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