A visual representation of the volume element and a numerical tool for calculating integrals of scalar and vector fields

This interactive demonstration that provides a visual and numerical explanation of volume integrals. The first part of the demo, built with Three.js, focuses on the concept of an infinitesimal volume element (dV) in a 3D Cartesian coordinate system. It displays an interactive 3D cube representing this element, which users can rotate and zoom. Input fields allow users to change the dimensions (dx, dy, dz), and the demo dynamically updates the cube's size and calculates the total volume (dV = dx * dy * dz) in real time. The second part of the demo provides a practical tool for calculating volume integrals over a defined rectangular domain. It uses Riemann sums to approximate the integral for both scalar and vector fields. Users can set the integration range (x, y, z min/max) and the number of steps per dimension to control the accuracy.

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