Gauss-Kronrod Quadrature Calculator

Let $f(x)$ be a function of real numbers and its derivative, $f'(x)$, exists in the interval $(a,b)$. If $a$ and $b$ are not singular points (the points where $f(x)$ or $f'(x)$ do not exist or are not finite), this application use Gauss-Kronrod quadrature method to calculate the numerical integration $I$: \[ I = \int_a^b f(x)\;\mathrm{d}x \]

In the case $a$ and/or $b$ are singular, it is recommended to use the calculator Double-Exponential Quadrature

For example, $f(x)=1-x^2$ and $a=0,b=1$, using this calculator we get \[ I=\int_0^1 (1-x^2)\;\mathrm{d}x = 0.6667 \]

Input Data

The input for function $f(x)$ is the same as in function derivative. The lower limit and upper limit of the integration $a,b$ are input as real numbers, e.g. 2 3.14 or math expression like 2^3 sin(pi/3) sqrt(pi). If $a$ or $b$ (but not both) is infinite, enter it as inf for $\infty$ and -inf for $-\infty$.

Gauss-Kronrod Quadrature Calculator