Gaussian Area Approximation Using Riemann Rectangles .... تَقْرِيبُ المَسَاحَةِ تَحْتَ الدَّالَّةِ الغَاوْسِيَّةِ بِمُسْتَطِيلَاتِ رِيمَان

This animation provides a clear, intuitive visualization of numerical integration using midpoint Riemann rectangles. The top graph displays the rectangles updating in real time as their width changes, while the bottom graph shows the exact area under the same curve for comparison. A live numerical value updates throughout the animation, allowing viewers to see how the approximation improves with smaller subdivisions. The code is fully commented and structured for easy modification, making it a great tool for teachers, students, and content creators who want to explain numerical integration visually and effectively.