Given a target accuracy $ \epsilon $, the integral of
a function $ f $ between $ a $ and $ b $ is
calculated by means of the trapezoid formula
$$
\int_{a}^{b} f \mathrm{d}x =
\frac{1}{2} f(x_{0}) + f(x_{1}) + f(x_{2}) + \dots
f(x_{N-1}) + \frac{1}{2} f(x_{N})
$$
where $ x_0 = a $, $ x_N = b $, and
$ x_i = a+i \Delta x $ with
$ \Delta x = (b-a)/N $. The number $ N $ of intervals
is repeatedly increased until the target accuracy is reached.
test
the correctness of the result is tested by checking it
against known good values.
Integral of a one-dimensional function
Given a target accuracy $ \epsilon $, the integral of a function $ f $ between $ a $ and $ b $ is calculated by means of the trapezoid formula $$ \int_{a}^{b} f \mathrm{d}x = \frac{1}{2} f(x_{0}) + f(x_{1}) + f(x_{2}) + \dots
the correctness of the result is tested by checking it against known good values.