Ďakujeme za prednášky: doc. Chovanec, doc. Dedera a cvičenia Dr. Ondis:

https://hrubos.tech/blogy/content/images/20260127115924-geometricky-integral-solution.png

https://hrubos.tech/blogy/content/images/20260127120027-geometricky-integral-sol-numeric.png

using Pkg
Pkg.add("Plots")

using Plots

# interval boundaries
a = 0.0
b = log(2)

# number of rectangles
n = 40
Δx = (b - a) / n

# x positions (left Riemann sum)
xs = a:Δx:(b - Δx)

# functions
f(x) = exp(2x)
g(x) = exp(x)

# rectangle heights
heights = f.(xs) .- g.(xs)

# Riemann sum (area approximation)
area = sum(heights .* Δx)
println("Approximate area = ", area)

# fine grid for smooth curves
xplot = range(a, b, length = 400)

# create plot
plt = plot(
    xplot,
    f.(xplot),
    label = "y = e^{2x}",
    linewidth = 2
)

plot!(
    plt,
    xplot,
    g.(xplot),
    label = "y = e^x",
    linewidth = 2
)

# Riemann rectangles
bar!(
    plt,
    xs,
    heights,
    width = Δx,
    bottom = g.(xs),
    opacity = 0.4,
    label = "Riemann rectangles"
)

xlabel!(plt, "x")
ylabel!(plt, "y")
#title!(plt, "Geometric Riemann Sum: Area between e^x and e^{2x}")
# correct title with interpolation
title!(
    plt,
    "Approximate area = $(round(area, digits=6))\narea = sum(heights .* Δx)"
)

# save to PNG
savefig(plt, "riemann_area.png")
println("Plot saved as riemann_area.png")

println("Press Enter to exit...")
readline()

---