- that the
variable of
integration is x. The
function f(x) is
called the
integrand, the
points a and b are
called the
limits (or bounds) of integration,...
-
stochastic generalization of the Riemann–Stieltjes
integral in analysis. The
integrands and the
integrators are now
stochastic processes: Y t = ∫ 0 t H s d X...
-
opposed to
analytical integration by
finding the antiderivative: The
integrand f (x) may be
known only at
certain points, such as
obtained by sampling...
-
numerical integration (also
called quadrature)
based on
evaluating the
integrand at
equally spaced points. They are
named after Isaac Newton and Roger...
- Simpson's rule
gains an
extra order because the
points at
which the
integrand is
evaluated are
distributed symmetrically in the
interval [ a , b ]...
-
algorithms usually evaluate the
integrand at a
regular grid,
Monte Carlo randomly chooses points at
which the
integrand is evaluated. This
method is particularly...
- for
integrable functions with
endpoint singularities. Instead, if the
integrand can be
written as f ( x ) = ( 1 − x ) α ( 1 + x ) β g ( x ) , α , β >...
- The
following is a list of
integrals (antiderivative functions) of
trigonometric functions. For
antiderivatives involving both
exponential and trigonometric...
-
traditional algorithms for "well behaved"
integrands, but are also
effective for "badly behaved"
integrands for
which traditional algorithms may fail...
- {\frac {1}{ax^{2}+bx+c}}\,dx+C} The
resulting integrands are of the same form as the
original integrand, so
these reduction formulas can be repeatedly...
