Task: Active object
C#: using System;
using System.Threading.Tasks;

using static System.Diagnostics.Stopwatch;
using static System.Math;
using static System.Threading.Thread;

class ActiveObject
{
    static double timeScale = 1.0 / Frequency;

    Func<double, double> func;
    Task updateTask;
    double integral;
    double value;
    long timestamp0, timestamp;

    public ActiveObject(Func<double, double> input)
    {
        timestamp0 = timestamp = GetTimestamp();
        func = input;
        value = func(0);
        updateTask = Integrate();
    }

    public void ChangeInput(Func<double, double> input)
    {
        lock (updateTask)
        {
            func = input;
        }
    }

    public double Value
    {
        get
        {
            lock (updateTask)
            {
                return integral;
            }
        }
    }

    async Task Integrate()
    {
        while (true)
        {
            await Task.Yield();
            var newTime = GetTimestamp();
            double newValue;

            lock (updateTask)
            {
                newValue = func((newTime - timestamp0) * timeScale);
                integral += (newValue + value) * (newTime - timestamp) * timeScale / 2;
            }

            timestamp = newTime;
            value = newValue;
        }
    }
}

class Program
{
    static Func<double, double> Sine(double frequency) =>
        t => Sin(2 * PI * frequency * t);

    static void Main(string[] args)
    {
        var ao = new ActiveObject(Sine(0.5));
        Sleep(TimeSpan.FromSeconds(2));
        ao.ChangeInput(t => 0);
        Sleep(TimeSpan.FromSeconds(0.5));
        Console.WriteLine(ao.Value);
    }
}

Java: 
public class Integrator {

    public interface Function {
        double apply(double timeSinceStartInSeconds);
    }

    private final long start;
    private volatile boolean running;

    private Function func;
    private double t0;
    private double v0;
    private double sum;

    public Integrator(Function func) {
        this.start = System.nanoTime();
        setFunc(func);
        new Thread(this::integrate).start();
    }

    public void setFunc(Function func) {
        this.func = func;
        v0 = func.apply(0.0);
        t0 = 0;
    }

    public double getOutput() {
        return sum;
    }

    public void stop() {
        running = false;
    }

    private void integrate() {
        running = true;
        while (running) {
            try {
                Thread.sleep(1);
                update();
            } catch (InterruptedException e) {
                return;
            }
        }
    }

    private void update() {
        double t1 = (System.nanoTime() - start) / 1.0e9;
        double v1 = func.apply(t1);
        double rect = (t1 - t0) * (v0 + v1) / 2;
        this.sum += rect;
        t0 = t1;
        v0 = v1;
    }

    public static void main(String[] args) throws InterruptedException {
        Integrator integrator = new Integrator(t -> Math.sin(Math.PI * t));
        Thread.sleep(2000);

        integrator.setFunc(t -> 0.0);
        Thread.sleep(500);

        integrator.stop();
        System.out.println(integrator.getOutput());
    }
}