The modern method consists of numerical integration in 3-dimensional space.

Numerical integration was often easier than trying to find closed form solutions for difficult problems.

This fact can also be used for numerical integration.

Some embedded systems and other computer applications may need numerical integration for this reason.

Normally these are complicated functions and numerical integration is needed.

There are several reasons for carrying out numerical integration.

This model is not solvable in closed form and instead requires numerical integration.

This is called a composite rule, see Numerical integration.

At least three methods of numerical integration can be phrased as follows.

Such topics may include Fourier analysis, numerical integration, or other required skills.

In most realistic cases, numerical integration is required to compute the integral.

Numerical integration of phytoplankton through depth and time in a water column.

However, the numerical integration of these terms will hardly lead to the same result, because the solution is approximated.

One common application of weighted sums arises in numerical integration.

He is credited with a formula for numerical integration.

Step 3) Obtain net work (a single number) by numerical integration of muscle power data.

In general, solutions are found by numerical integration.

However, they can be estimated by numerical integration.

For more awkward distributions, numerical integration may be required.

Long-term numerical integration shows that the orbit is stable.

The method requires the use of differential equations, specifically numerical integration methods.

Approximation errors due to the selection of numerical integration algorithm.

The goals of numerical integration are accuracy, reliability, efficiency, and generality.

See Truncation error (numerical integration) for more on this.

If one treats this system on a short interval, e.g. there is no problem in numerical integration.