Numerical Integration

torapezoidal_integration.jl

using Base.Test


function integrate(f, a, b, n_samples=100)
    assert(b > a)
    h = (b - a) / n_samples
    xs = linspace(a, b, n_samples)
    ys = [f(x) for x in xs]
    h * ((ys[1] + ys[end]) / 2 + sum(ys[2:end-1]))
end


function test_integrate()
    @test abs(integrate(sin, 0, 2π, 100) - 0) < 1e-8
    @test abs(integrate(cos, 0, π/2, 1e5) - 1) < 1e-3
end


function run_homework()
    println(
        "Integration of 4 / (1 + x^2)            in range [0, 1]   : " *
        "$(integrate(x -> 4 / (1+x^2), 0, 1, 10))"
    )
    println(
        "Integration of sin(100x) + sin(57x) + 5 in range [0, π/2] : " *
        "$(integrate(x -> sin(100x) + sin(57x) + 5, 0, π/2, 10))"
    )
end

test_integrate()
run_homework()