Does space-time have an energy itself?

[marcus]

I'm glad you can use Desmos. I think it is excellent. I will look for an online utility that can do integrals. Do you by any chance know of one.?

Let me know if any of my explanations in this thread are hard to follow, or confusing. I'll try to make them clearer.
I live in California and the time is called "pacific time" Your time, I think, is about 10 hours ahead.

In my local time it is about 10:30 PM as I post this now.

 

[Quarlep]

Here time is 08:31 in the morning.I don't know integral online calculator but I can find. I read your new thread its really helped me to understand deeper.

 

[marcus]

Here time is 08:31 in the morning.I don't know integral online calculator but I can find. I read your new thread its really helped me to understand deeper.

Here it is 10:52 PM in the evening. That means you are 10 hours ahead.
Thanks for the encouragement. I found an online numerical integration website that does definite integrals between lower and upper limits
http://www.webmath.com/nintegrate.html
It is very minimal. The integrand must be defined with just a few characters

 

[marcus]

At that "web math" site I was able to integrate
(sinh(1.5x)^(-2/3) between limits .1 and .8
but they would not let me type in more characters so I could not integrate
1.311(sinh(1.5x)^(-2/3)
that was too long for them

 

[Quarlep]

http://www.integral-calculator.com look this maybe it helps I calculate 1.311sinh(1.5x)^(-2/3) and it gave me result but indefinite integral I guesss you can make definite to click options

 

[marcus]

that's interesting. I'll go look at it.
I found something that does definite integrals just now that seems good:
http://www.numberempire.com/definiteintegralcalculator.php

It has plenty of room to input the integrand, no unreasonable character limit.

as a test, I did 1.311(sinh(1.5x))^(-2/3) from 0.1 to 0.797 and it gave 1.33100...
It seems easy to use and simple. Not a lot of extras

EDIT (at 11:42 PM pacific time). It's late now, so I'm turning in.

 

[marcus]

Now 6AM pacific, I want to check out that "numberempire" numerical integrator a bit more
Wondering if it has other hyper-trig functions like hyperbolic secant ("sech(x)")
*************************
"numberempire" is actually pretty nice.
It goes way beyond the small job we have for it which is basically integrating the stretch factor S(x) = 1/a(x) = 1.311/sinh(1.5x)^2/3

In trig you may have encountered a special name for 1/sin, it is called "cosecant" and abbreviated "csc".
When I was in school it seemed to me needlessly fussy to have a special name for 1/sin.
I think it goes back to the days before computers when people worked with TRIG TABLES and it might save you a step in the calculation to have 1/sin already tabulated.

Anyway numberempire knows "csch" the hyperbolic cosecant so even though it may seem silly or unnecessarily fancy we can write the stretch factor S(x) as
S(x) = 1.311 csch(1.5x)^2/3

If I integrate that from .1 to .797 it is the distance NOW a flash of light can have traveled if emitted at time x = 0.1 (if not scattered or absorbed, if allowed to travel freely)
And I can multiply by 17.3 to get the answer in billions of light years. Here is how it looks when the Empire does the integral for us.
This page is live so you can put in x=0.2 and calculate for that, and put in 0.3 and calculate, and so on.
http://www.numberempire.com/definiteintegralcalculator.php?function=17.3*1.311*csch(1.5*x)^(2/3)&var=x&a=.1&b=.797&answers=

Here it is for x=0.2:
http://www.numberempire.com/definiteintegralcalculator.php?function=17.3*1.311*csch(1.5*x)^(2/3)&var=x&a=.2&b=.797&answers=

 

[Quarlep]

I am looking through my phone I ll look as soon as possible

 

[marcus]

I am looking through my phone I ll look as soon as possible

It may be that the search is over and it isn;t necessary to look further. I have had some experience with "Number Empire" numerical definite integral and I really like it. It is a simply presented powerful tool. My impression is that it is reliable. Of course I could be mistaken.
http://www.numberempire.com/definiteintegralcalculator.php
When you have time, check to see if you can get it, where you live. If you find it useful we don't have to look any more.

The place where you type in the function to be integrated, and the upper and lower limits, is right at the top of the page. It is direct, they don't distract the user with other stuff.

 

[Quarlep]

Yeah I got my questions answer.Again thank you.I look at it and its good integral calculater thanks for that too.