# 16.8 2D Volume Integrate (Pro Only)

## Overview

2D Volume Integration tool calculates the volume between the plane Z=0 and the matrix surface, by two-dimensional integration. Two-dimensional volume integration can be performed on a matrix window or on a plot of matrix data.

##### To Use 2D Volume Integration Tool
1. Create a new matrix with data.
2. Activate the matrix.
3. Select Analysis: Mathematics: 2D Volume Intergrate from the Origin menu to open the integ2 dialog.
4. Choose your options and click OK. The X-Function integ2 is called to perform the calculation.

## Dialog Options

Input Matrix The operating matrix. Trim missing values if this parameter is true.

## Algorithm

This function computes the volume beneath the matrix surface using a numeric integral method.

For a continuous surface $z=f(x,y),(x,y)\in \sigma$, the volume beneath it can be computed as:

$\iint_{(\sigma)}f(x,y)dxdy$,

Using a numeric method, it can be written as:

$\iint_{(\sigma)}f(x,y)dxdy=\lim_{\Delta x \to 0}\lim_{\Delta y \to 0} \sum_{i=0}^{m-1} \sum_{j=0}^{n-1} f(x_{i,}y_j)\Delta x\Delta y\approx \sum_{i=0}^{m-1} \sum_{j=0}^{n-1} f(x_i,y_j)\Delta x\Delta y$

where the M, N is the number of the rows and columns of the matrix respectively. In the actual process of computing,

$\left( f\left( x_i,y_j\right) +f(x_i,y_{j+1})+f(x_{i+1},y_j)+f(x_{i+1},y_{j+1})\right)/ 4$

is used instead of $f(x_i,y_j)\!$.