# 
## Overview

**SciPy** is an open-source library provided by **Python** that is dedicated to scientific computation.

**`scipy.integrate`** is a sub-package in SciPy that provides the functionality to solve several integration methods, including Ordinary Differential Equations (ODEs). 

We can use the **`scipy.integrate.dblquad`** method in SciPy to solve general-purpose double integration.


## Syntax

```Python
scipy.integrate.dblquad(func, a, b, gfun, hfun, args=(), epsabs=1.49e-08, epsrel=1.49e-08)
``` 

## Parameters

* **`func`**: This is a Python function or method that represents a double integral function. It takes at least two inputs that acts as variables to the double integral. Given the variables $x$ and $y$, it takes $y$ as the first argument, and $x$ as the second argument.

* **`a,b`**: These are the integration limits in $x$ where $a<b$. Both have the type **`float`**.
* **`gfun`**: This is a Python function or `float` that represents the lower boundary curve in $y$, which is a function of $x$. It returns a single floating-point value.

* **`hfun`**: This is a Python function or `float` that represents the higher boundary curve in $y$, which is a function of $x$. It returns a single floating-point value.

* **`args`**: This is an optional parameter that is a sequence of extra arguments passed to `func`.

* **`epsabs`**: This is an optional parameter that is the absolute tolerance passed directly to the inner 1-D quadrature integration. Its default is $1.49e-8$.

* **`epsrel`**: This is an optional parameter that is the relative tolerance of the inner 1-D integrals. Its default is $1.49e-8$.

## Return value

**`y`**: It is the computed double definite integral of **`func(y,x)`**. It has the type `float`.

**`abserr`**: It is an estimate of the error. It has the type `float`.


## Example

Let's see how to compute the double intergal of $f(y,x) = xy^4$ using the `scipy.integrate.dblquad` method, where $x$ ranges from $0$ to $2$, and $y$ ranges from $0$ to $1$.



from scipy import integrate
func = lambda y, x: x*y**4
print(integrate.dblquad(func, 0, 2, lambda x: 0, lambda x: 1))

## Explanation
- **Line 1**: We import **`integrate`** from **`scipy`**.
* **Line 2**: We write the lambda function **`func`**. It takes two inputs where `y` is the first argument and `x` is the second argument.

* **Line 3**: We use the `scipy.integrate.dblquad` method. It returns the double (definite) integral of `func` over the region, where $x$ is from $0$ to $2$ and $y$ is from $0$ to $1$. 

>**Note**: We write the constant boundary curve for $y$ as a lambda function of $x$ 

What is the scipy.integrate.dblquad method in Python?

Overview

Syntax

Parameters

Return value

Example

Explanation