Visualize integral 2025 as area under the curve (Mathematica)#1
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Visualize integral 2025 as area under the curve (Mathematica)#1raypereda wants to merge 1 commit into
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Visualizes Integrate[4^x/(4^x+2), {x,0,1}] = 1/2 with:
- exact symbolic integration
- a symbolic proof that f(x)+f(1-x)==1 (why the area is exactly 1/2)
- a filled area-under-curve plot
- an interactive midpoint Riemann-sum Manipulate
- a reflection/tiling picture showing the area is half a unit square
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01LhzuZxgPBzeNeZqBLFcHEb
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Summary
Adds
integral-2025-visualization.wl, Mathematica code that visualizesas the area under the curve (the photo's
2025 × integral = 1012.5is just2025/2).What it leverages from Mathematica
Integratereturns1/2, no quadrature error.FullSimplify[f[x] + f[1-x] == 1]returnsTrue, which is why the area is exactly one half.1/2.Manipulate) converging to the exact value.fand its 180° rotation about(1/2, 1/2)tile the unit square, so the area is half of it.Notes
Code is in plain
.wl(Wolfram Language) so it diffs/reviews cleanly; paste into a Mathematica notebook (or run withwolframscript) to see the interactive elements.🤖 Generated with Claude Code
https://claude.ai/code/session_01LhzuZxgPBzeNeZqBLFcHEb
Generated by Claude Code