WIP: Add demonstrative examples to documentation

[mikeingold]

Preview: https://juliageometry.github.io/MeshIntegrals.jl/previews/PR201/

[github-actions]

Benchmark Results (Julia v1.10)

Time benchmarks

	main	2a15296...	main / 2a15296...
Differentials/Differential	0.207 ± 0.002 μs	0.205 ± 0.0011 μs	1.01 ± 0.011
Differentials/Jacobian	0.17 ± 0.001 μs	0.17 ± 0.001 μs	1 ± 0.0083
Integrals/Segment/Scalar GaussKronrod	0.691 ± 0.001 μs	0.621 ± 0.011 μs	1.11 ± 0.02
Integrals/Segment/Scalar GaussLegendre	1.74 ± 0.01 μs	1.8 ± 0.031 μs	0.967 ± 0.018
Integrals/Segment/Scalar HAdaptiveCubature	0.832 ± 0.029 μs	0.812 ± 0.08 μs	1.02 ± 0.11
Integrals/Segment/Vector GaussKronrod	0.652 ± 0.01 μs	0.652 ± 0.01 μs	1 ± 0.022
Integrals/Segment/Vector GaussLegendre	4.72 ± 0.3 μs	4.74 ± 0.27 μs	0.996 ± 0.085
Integrals/Segment/Vector HAdaptiveCubature	0.882 ± 0.031 μs	0.861 ± 0.03 μs	1.02 ± 0.051
Integrals/Sphere/Scalar GaussKronrod	1.12 ± 0.01 μs	1.12 ± 0.01 μs	1 ± 0.013
Integrals/Sphere/Scalar GaussLegendre	1.87 ± 0.0064 ms	1.88 ± 0.01 ms	0.996 ± 0.0065
Integrals/Sphere/Scalar HAdaptiveCubature	0.048 ± 0.00011 ms	0.0478 ± 0.00012 ms	1 ± 0.0034
Integrals/Sphere/Vector GaussKronrod	1.14 ± 0.001 μs	1.15 ± 0.01 μs	0.991 ± 0.0086
Integrals/Sphere/Vector GaussLegendre	2.03 ± 0.015 ms	2.04 ± 0.016 ms	0.997 ± 0.011
Integrals/Sphere/Vector HAdaptiveCubature	0.0491 ± 0.00011 ms	0.0492 ± 0.00011 ms	0.998 ± 0.0032
Rules/GaussLegendre	21.7 ± 0.51 μs	22.1 ± 0.53 μs	0.983 ± 0.033
Specializations/Scalar GaussLegendre/BezierCurve	0.251 ± 0.007 ms	0.245 ± 0.007 ms	1.02 ± 0.041
Specializations/Scalar GaussLegendre/Line	6.92 ± 0.081 μs	7.12 ± 0.06 μs	0.972 ± 0.014
Specializations/Scalar GaussLegendre/Plane	0.745 ± 0.0021 ms	0.745 ± 0.0023 ms	0.999 ± 0.0042
Specializations/Scalar GaussLegendre/Ray	5.87 ± 0.06 μs	5.9 ± 0.05 μs	0.995 ± 0.013
Specializations/Scalar GaussLegendre/Rope	0.0507 ± 0.00028 ms	0.0506 ± 0.00026 ms	1 ± 0.0076
Specializations/Scalar GaussLegendre/Tetrahedron	0.155 ± 0.00098 s	0.156 ± 0.0011 s	0.999 ± 0.0093
Specializations/Scalar GaussLegendre/Triangle	0.642 ± 0.008 ms	0.715 ± 0.015 ms	0.897 ± 0.022
time_to_load	1.49 ± 0.019 s	1.49 ± 0.027 s	1 ± 0.022

Memory benchmarks

	main	2a15296...	main / 2a15296...
Differentials/Differential	3 allocs: 0.0938 kB	3 allocs: 0.0938 kB	1
Differentials/Jacobian	0 allocs: 0 B	0 allocs: 0 B
Integrals/Segment/Scalar GaussKronrod	2 allocs: 0.0469 kB	2 allocs: 0.0469 kB	1
Integrals/Segment/Scalar GaussLegendre	0 allocs: 0 B	0 allocs: 0 B
Integrals/Segment/Scalar HAdaptiveCubature	7 allocs: 0.492 kB	7 allocs: 0.492 kB	1
Integrals/Segment/Vector GaussKronrod	2 allocs: 0.0781 kB	2 allocs: 0.0781 kB	1
Integrals/Segment/Vector GaussLegendre	0.307 k allocs: 12.8 kB	0.307 k allocs: 12.8 kB	1
Integrals/Segment/Vector HAdaptiveCubature	6 allocs: 0.688 kB	6 allocs: 0.688 kB	1
Integrals/Sphere/Scalar GaussKronrod	2 allocs: 0.0469 kB	2 allocs: 0.0469 kB	1
Integrals/Sphere/Scalar GaussLegendre	0 allocs: 0 B	0 allocs: 0 B
Integrals/Sphere/Scalar HAdaptiveCubature	7 allocs: 0.648 kB	7 allocs: 0.648 kB	1
Integrals/Sphere/Vector GaussKronrod	2 allocs: 0.0781 kB	2 allocs: 0.0781 kB	1
Integrals/Sphere/Vector GaussLegendre	30 k allocs: 1.22 MB	30 k allocs: 1.22 MB	1
Integrals/Sphere/Vector HAdaptiveCubature	6 allocs: 0.812 kB	6 allocs: 0.812 kB	1
Rules/GaussLegendre	7 allocs: 0.0325 MB	7 allocs: 0.0325 MB	1
Specializations/Scalar GaussLegendre/BezierCurve	23 allocs: 0.75 kB	23 allocs: 0.75 kB	1
Specializations/Scalar GaussLegendre/Line	21 allocs: 0.938 kB	21 allocs: 0.938 kB	1
Specializations/Scalar GaussLegendre/Plane	22 allocs: 1.03 kB	22 allocs: 1.03 kB	1
Specializations/Scalar GaussLegendre/Ray	21 allocs: 0.938 kB	21 allocs: 0.938 kB	1
Specializations/Scalar GaussLegendre/Rope	0.068 k allocs: 1.62 kB	0.068 k allocs: 1.62 kB	1
Specializations/Scalar GaussLegendre/Tetrahedron	3 M allocs: 0.179 GB	3 M allocs: 0.179 GB	1
Specializations/Scalar GaussLegendre/Triangle	22 allocs: 1.03 kB	22 allocs: 1.03 kB	1
time_to_load	0.153 k allocs: 14.5 kB	0.153 k allocs: 14.5 kB	1