Mathematics |

**Example: Double Integration**

Consider the numerical solution of

For this example

. The first step is to build the function to be evaluated. The function must be capable of returning a vector output when given a vector input. You must also consider which variable is in the inner integral, and which goes in the outer integral. In this example, the inner variable is *x *and the outer variable is *y* (the order in the integral is *dxdy*). In this case, the integrand function is

To perform the integration, two functions are available in the `funfun`

directory. The first, `dblquad`

, is called directly from the command line. This M-file evaluates the outer loop using `quad`

. At each iteration, `quad`

calls the second helper function that evaluates the inner loop.

To evaluate the double integral, use

The first argument is a string with the name of the integrand function. The second to fifth arguments are

`xmin` |
Lower limit of inner integral |

`xmax` |
Upper limit of the inner integral |

`ymin` |
Lower limit of outer integral |

`ymax` |
Upper limit of the outer integral |

Here is a numeric example that illustrates the use of `dblquad`

.

By default, `dblquad`

calls `quad`

. To integrate the previous example using `quadl`

(with the default values for the tolerance argument), use

Alternatively, you can pass any user-defined quadrature function name to `dblquad`

as long as the quadrature function has the same calling and return arguments as `quad`

.

Example: Computing the Length of a Curve | Differential Equations |