*Last updated: 2023-03-16.*
# tf_quant_finance.math.integration.simpson
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Evaluates definite integral using composite Simpson's 1/3 rule.
```python
tf_quant_finance.math.integration.simpson(
func, lower, upper, num_points=1001, dtype=None, name=None
)
```
Integrates `func` using composite Simpson's 1/3 rule [1].
Evaluates function at points of evenly spaced grid of `num_points` points,
then uses obtained values to interpolate `func` with quadratic polynomials
and integrates these polynomials.
#### References
[1] Weisstein, Eric W. "Simpson's Rule." From MathWorld - A Wolfram Web
Resource. http://mathworld.wolfram.com/SimpsonsRule.html
#### Example
```python
f = lambda x: x*x
a = tf.constant(0.0)
b = tf.constant(3.0)
simpson(f, a, b, num_points=1001) # 9.0
```
#### Args:
* `func`: Represents a function to be integrated. It must be a callable of a
single `Tensor` parameter and return a `Tensor` of the same shape and
dtype as its input. It will be called with a `Tensor` of shape
`lower.shape + [n]` (where n is integer number of points) and of the same
`dtype` as `lower`.
* `lower`: Represents the lower limits of integration. `func` will be integrated
between each pair of points defined by `lower` and `upper`.
* `upper`: Same shape and dtype as `lower` representing the upper limits of
intergation.
* `num_points`: Number of points at which function `func` will be evaluated.
Must be odd and at least 3. Default value: 1001.
* `dtype`: If supplied, the dtype for the `lower` and `upper`. Result will have
the same dtype.
Default value: None which maps to dtype of `lower`.
* `name`: The name to give to the ops created by this function.
Default value: None which maps to 'integrate_simpson_composite'.
#### Returns:
`Tensor` of shape `func_batch_shape + limits_batch_shape`, containing
value of the definite integral.