How do I do this Integral in Geogebra Classic?

GeoSwan shared this question 2 years ago

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I have this specific integral that I desire to replicate in GeoGebra, which is made in another graphing calculator. I was wondering if there is anyway to get an exact match to this?

Files: Integral vel.png

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Comments (10)

ccambre ● 2 years ago

The f(x) and c used in the calculation are nit shown and in many cases it's undefined.

you can calculate the integral as Integral(sqrt(1-f²/c²), 0, 20000).

If you want to display formula and result of the integral, you can do it as a Textobject using LaTeX. I used random values for f and c that produce a defined solution

Files: integral.ggb

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GeoSwan ● 2 years ago

Seems that it does not work with the integral I'm using. It's says "undefined" in places that it should be doing if done correctly.

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GeoSwan ● 2 years ago

Fixed now, the issue was the x start coordinate. Thx :)

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Michael Borcherds ● 2 years ago

Please post your .ggb file

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GeoSwan ● 2 years ago

I have done so below.

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mathmagic ● 2 years ago

what is f ?

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GeoSwan ● 2 years ago

Thank you for answering. However it does not seem to be working right now. I'll try posting the ggb file and explain a bit about the problem I'm trying to solve, because the graph that I'll post might look a bit complicated at first glance, plus I think it's a fairly unique use of some of GeoGebra's new features that I'm trying to apply towards some interesting physics problems.

I have constructed an Ellipse whose size is adjustable by the top left slider. The parameter currently typed are an exact match for the known values of the object. ie Semi-Major Axis (SMA), Eccentricity, Minor axis etc. An object obeying all of Kepler's laws have been placed along the Ellipse, the object is Pluto and the central body is the Sun.

Using the vis-viva equation I'm generating a Speed versus Time graph of the planet through one full orbital cycle, by using the trace function and plotting the velocity curve by recording all the traces of Point(Q) to the spreadsheet. Then I'm using the linegraph command to transform all these point into a smooth function which I desire to put as the v component in the relativistic Lorentz equation that I linked earlier.

I basically want an integral that sums up the total kinematic time dilation occurring over one the full orbital cycle, where the f(x) function acts as our velocity squared component.

The f(x) used in the previous attachment will in this file be named h(x) and is our velocity curve in Km/s. C in the integral is the speed of light. dx is time component which denotes the orbital cycle in years.

Files: Generalized Pla...

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Michael Borcherds ● 2 years ago

This seems to work fine in your file:

Integral(1-(h(x))^2/100,0.01,240)

What isn't working exactly?

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GeoSwan ● 2 years ago

I'll try it.

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GeoSwan ● 2 years ago

Yes, modifying your integral, so that the units are correct yields the correct result. Thank you.

The integral then becomes:

Integral(1-((h(x)*1000)^2/299792458^2),0.0005,246.95572)

which gives 246.95532, that looks like the right result at first glance.

I'm assuming that all my troubles came from me setting the X start-coordinate to 0 instead of 0.01 or 0.0005 . That seems to mess up the expression. I might have screwed up a single bracket as well.

Again, thank you for taking the time to look over my problem, now I can continue my planetary velocity research with no hindrance :smile: cheers.

Fun fact: The total kinematic time dilation for Pluto turned out to be around 210 minutes per orbital cycle, which takes approx. 247 years.

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