Double Integrals

## Description

For a multivariable function $f(x,y)$ we can calculate the double integral

(1)\begin{align} \int\int f(x,y) \space dy dx = \int \left(\int f(x,y) dy\right) dx \end{align}

which represents the area under the rectangle. The Sage cell below calculates the double integral of $\int_0^2 \int_0^1 f(x, y) = 8x + 6y \space dx dy.$

## Sage Cell

#### Code

```
var("y")
f(x, y) = 8*x + 6*y
integral(integral(f(x, y), x, 0, 1), y, 0, 2)
```

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Date: 06 Nov 2018 20:27

Submitted by: James A Phillips