# quadv

Numerical integration using adaptive Simpson's rule.

## Syntax

area=quadv(@func,a,b)

area=quadv(@func,a,b,abstol)

[area,count]=quadv(...)

## Inputs

`func`- The function to integrate.
`a`- Lower integration limit.
`b`- Upper integration limit.
`abstol`- Absolute tolerance (default: sqrt(eps) or about 1.0e-8).

## Outputs

- area
- The estimated area.
- count
- Number of function evaluations.

## Examples

Single
interval:

```
function y = Integrand(x)
y = 13 * (x - x^2) * exp(-3*x/2);
end
[area,count] = quadv(@Integrand, 0, 4, 1.0e-5)
```

```
area = -1.54878858
count = 69
```

Multiple intervals with an anonymous function:

`[area,count] = quadv(@(x) sqrt(x), [0, 1], [1, 2])`

```
area = [Matrix] 1 x 2
0.66667 1.21895
count = [Matrix] 1 x 2
309 29
```

## Comments

quadv recursively bisects each interval until the improvement from the bisections falls below the absolute tolerance. Intervals are assumed to have finite bounds.

The maximum number of function evaluations is 10,000, and the minimum interval is 1.0e-12.

To pass additional parameters to a `function` argument, use an
anonymous function.

quadv does not yet support `func` returning a matrix to
support multiple simultaneous integrands.