**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 defined on closed interval let be the function given by

The is uniformly continuous on , differentiable on the open interval , and

## 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

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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 🙂