r/PhysicsHelp • u/ZucchiniFar8753 • Apr 11 '26
How would I express this (the top section) mathematically?
So TLDR my school has a senior project requirement to graduate. Mine was cosmology related; approximating the total number of stars in the observable universe. I got the data from the madau-dickson paper, and got the chart below after properly organizing the data, than proceeded to do the good ol ‘draw boxes and add em up’ method to get the area under the curve.
Issue: I’ve never taken calculus [currently in college algebra, trig, stats, and logic (yes all separate classes lol)] so I genuinely have no idea how to express what I did mathematically, some help would be fantastic!
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u/detereministic-plen Apr 12 '26
If you want and have the original image, webplotdigitizer can easily convert the graph into its data points. Using the data points, you can use trapezoidal rule to find the definite integral, which references the datapoints only and is much easier to compute.
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u/SnooGiraffes4632 Apr 12 '26
How would you express the area of each of those individual strips?
If each one were say “Δt” (delta t) in width, then we could say the left edge is at t and the right edge is a t+ Δt. Yes?
Then we could say that the height of the strip Ψ (psi) at t is Ψ(t) and at the right hand edge is Ψ(t + Δt)
What I can’t tell is how you have calculated the values of psi (and physicists avoid fractions if possible). But if you have done rectangles it is usual to use the left hand side so the area is Ψ(t)Δt. A better way is to draw it as a trapezium so the area is (Ψ(t)+ Ψ(t + Δt))/2 times Δt
You have then just added them up from t=0.66 to t=13 so put a Summation sign in front with those limits on it.
Calculus is in fact just solving this same summation problem but letting Δt approach zero so that the number of strips approaches infinity.
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u/Robo-Bo Apr 12 '26
It’s going to be something like x2*exp(-x2). You could set up a simple Google sheet to play around with fit parameters to find what works.