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POHow can you implement in java the mid-point rule (integration)?
 

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  1. POHow can you implement in java the mid-point rule (integration)?
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    <p>Taken from a lab : </p> <blockquote> <p>The aim of this exercise is to implement the midpoint-rule (also called rectangle method) >for the numerical integration of functions.</p> <p>Declare a generic interface Function as follows:</p> <p>public interface Function {B apply(A arg); }</p> <p>Then write a class Maths with a method integrate that implements the midpoint rule for a >function f that is to be integrated between lowerBound and upperBound in n equally-spaced >steps:</p> <p>public static double integrate(Function f, double lowerBound, double upperBound, int n)</p> <p>Test your code by numerical integration ofthe square-function between 0 and 1 (result should be approximately 1.0/3.0)</p> </blockquote> <h2> the sinus-function between 0 and PI/2 (see class java.lang.Math, result should be > approximately 1.0) It seems natural to use named local classes (say "Sinus" and "Square") for this exercise, > but you can also use anonymous local classes if you prefer.</h2> <p>I looked on the wikipedia page but I can't really get my head around the entire concept (especially what is meant by upper and lower bounds). Afaik it's just the way to get the area under a line, given N rectangles used to get the area for each tangential point on the line. I've no idea how to relate it to the above function - recursion maybe? and I've also never seen anything like :</p> <p>B apply(A arg)</p> <p>--</p> <p>So far I've made this progress:</p> <pre><code>public class MidPointRule { public MidPointRule() { } public static double integrate(Function&lt;Double,Double&gt; f, double lowerBound,double upperBound, int n){ double width = upperBound-lowerBound/n; // width is current width-nextwidth/n? return integrate(f,lowerBound,upperBound,n); } public static void main(String[] args) { // sq function between 0 and 1, sinus function between 0 and PI/2. } } </code></pre>
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    1. COThere are some questions which should be asked to classmates or responsible professor before being asked on StackOverflow. For questions on StackOverflow, we prefer that you show some progress of understanding the problem and show what you have tried.
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      1. USSimon Forsberg
    2. COnumerical methods in Java sounds so painful... That being said I don't think this is an SO related question...
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      1. POHow can you implement in java the mid-point rule (integration)?
      1. USMateusz Dymczyk
    3. CO@MateuszDymczyk that's why they have an interface for it, instead of making you interpret it from a string. You write the function right in java code.
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