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The `quad` function returns the adaptive Simpson quadrature approximation of a function. You must define a function that works for vector inputs and pass that function name to the `quad` function.

To use the `quad` function, you also pass the limits of integration that the function will use. Here's an example that returns the area under the curve defined in `my_function.m` over the range from a to b:

`    >> quad( 'my_function', 0, 10 )`

or

`    >> quad( @my_function, 0, 10 )`

Be sure to use element-wise (dot) operators in the function definition so that it will be evaluated correctly for vector input.

If your function requires additional constant input values, you will need to use a parameter for the constant and a different syntax. This is the same syntax used if additional parameters are required when using `fzero`. For example, to use `quad` to evaluate this function $my_function2\left(x,a\right)={\left(x-a\right)}^{2}-3$ for different values of `a`, like 5 or 8:

`    >> Q = quad( @(x)my_function2(x,5) , 0 , 2 );`
`    >> Q = quad( @(x)my_function2(x,8) , 0 , 2 );`

The `my_function2` function is defined as follows:

```    function y = my_function2( x , a )
y = (x - a).^2 - 3;
```