Fundamental Theorem of Calculus is a kind of a link between two most important calculus concepts: derivative and integral.
Fundamental Theorem of Calculus – formal statement
For continuous real-valued function $$f:[a,b]\to\mathbb{R}$$ defined on closed interval $$[a,b]$$ let $$F:[a,b]\to\mathbb{R}$$ be the function given by
$$F(x)=\int_a^x f(t)\text{d}t$$
The $$F$$ is uniformly continuous on $$[a, b]$$, differentiable on the open interval $$(a, b)$$, and
$$F'(x)=f(x)$$
Fundamental Theorem of Calculus – mXparser test
import org.mariuszgromada.math.mxparser.*;
...
/* Function */
Function f = new Function("f(x) = sin(x)");
/* Antiderivative */
Function F = new Function("F(x) = int(f(t), t, 0, x)", f);
/* function = derivative ( antiderivative ) */
Argument x = new Argument("x = pi");
Expression e = new Expression("f(x) - der(F(x), x)", x, f, F);
mXparser.consolePrintln("Res : " + e.getExpressionString() + " = " + e.calculate());
mXparser.consolePrintln("Computing time = " + e.getComputingTime() + " s.");
Res : f(x) - der(F(x), x) = 6.237833817291525E-8 Computing time = 0.411 s.
Best regards,
Mariusz Gromada
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Thanx a lot 🙂 Best regards – Mariusz
Hello, i feel that i saw you visited my website so i got here to go back the
prefer?.I’m trying to find issues to enhance my site!I assume its ok to use a few of your ideas!!
Sure, go ahead!
Can you give max length of formula string
Formula string is a String type – if limitation exist this is related to String class. Additionally internal iterators are “int” types, so forula length is definitely limited by max int 🙂
I need your help i use mxparser for a curve discussion programm, I use the 2nd derivation and sometimes it is Nan, although it shouldn’t be. Any idea to fix it?
Examples:
Expression e2 = new Expression(“solve( der( der(” + fkt + “, x), x), x, ” + z + “,” + (z + 1) + “)”, x);
Expression e2ex = new Expression(“solve( der( der(” + fkt + “, x), x), x, ” + i + “,” + (i + 1) + “)”, x);
Can you give the whole code? What is fkt, z, x, i?
ty for your fast response, here is the code:
/*
* To change this license header, choose License Headers in Project Properties.
* To change this template file, choose Tools | Templates
* and open the template in the editor.
*/
package projekt.syp;
import java.util.Iterator;
import java.util.Map;
import java.util.Set;
import java.util.TreeMap;
import java.util.TreeSet;
import javafx.scene.control.Alert;
import javafx.scene.control.Alert.AlertType;
import org.mariuszgromada.math.mxparser.Argument;
import org.mariuszgromada.math.mxparser.Expression;
/**
* @author laura
*/
public class Extrempunktrechner {
public static double eps = 0.0001;
/**
* @param args the command line arguments
*/
public static void main(String[] args) {
Map<String, Set> m = calcExtrem(“1/16*(x^4-24*x^2+128)”, “-5”, “5”);
for (String s : m.keySet()) {
System.out.println(s + “->” + m.get(s));
}
}
public static Map<String, Set> calcExtrem(String fkt, String minlimit, String maxLimit) {
Set hSet = new TreeSet(); //Set für Hochpunkte
Set tSet = new TreeSet(); //Set für Tiefpunkte
Set sSet = new TreeSet(); //Set für Sattelpunkte
Map<String, Set> extrem = new TreeMap(); //Map für alle Punkte
extrem.put(“Hochpunkt”, hSet);
extrem.put(“Tiefpunkt”, tSet);
extrem.put(“Sattelpunkt”, sSet);
Double min, max;
try {
min = Double.parseDouble(minlimit); //min und max in Double umwandeln
max = Double.parseDouble(maxLimit);
if (max < min) {
throw new NumberFormatException();
}
} catch (NumberFormatException nfe) {
Alert alert = new Alert(AlertType.ERROR); //Fehler falls min oder max keine Zahl oder max kleiner wie min
alert.setTitle("Min/Max Error!");
alert.setContentText("Min oder Max war keine Zahl!!");
alert.show();
return null;
}
for (double i = min; i <= max; i++) { //alle Werte im Intervall auf Extrempunkte überprüfen
Argument x = new Argument("x");
Expression e = new Expression("solve(der(" + fkt + ", x), x, " + i + "," + (i + 1) + ")", x);
double z = e.calculate(); //Wert der ersten Ableitung ausrechnen
Expression e2 = new Expression("solve( der( der(" + fkt + ", x), x), x, " + z + "," + (z + 1) + ")", x); //Zweite Ableitung
Expression e2ex = new Expression("solve( der( der(" + fkt + ", x), x), x, " + i + "," + (i + 1) + ")", x); //Falls irgendwie z Nan ist, jedoch die mit i ein Ergebnis rauskommen würde
double erg = e2.calculate(), ergx = e2ex.calculate(); //Ergebnis kalkulieren
if (erg < 0 || ergx 0 || ergx > 0) {
extrem.get(“Tiefpunkt”).add(e.calculate());
}
}
for (String s : extrem.keySet()) {
Iterator iterator = extrem.get(s).iterator(); //Iterator erzeugen zwecks entfernung von NaN werten
while (iterator.hasNext()) {
Double d = iterator.next();
if (Double.toString(d).equals(Double.toString(Double.NaN))) {
iterator.remove();
}
}
}
return extrem;
}
}
Ok – will look on that.
The problem is here.
You are trying to run “solve(der(1/16*(x^4-24*x^2+128), x), x, -5.0,-4.0)”, but
Function derf = new Function(“derf(x0) = der(1/16*(x^4-24*x^2+128), x, x0)”);
mXparser.consolePrintln(derf.calculate(-5));
mXparser.consolePrintln(derf.calculate(-4));
shows that derf do not change sign in “-5” and “-4”
[mXparser-v.4.2.0] -16.250000002983143
[mXparser-v.4.2.0] -4.000000002415618
thus it can not be solved numerically causing z = NaN
Oh, ty. Without you i wouldn’t have recognised this! TY!!!!!!!!!!!!!!!!!!!!!!!