Visualizing the Normal Distribution with Integral Area

This GeoGebra example demonstrates the visualization of the normal distribution (Gaussian distribution) curve and dynamically calculates the integral area under the curve for a given interval $[a, b]$, representing the probability. The core mathematical concepts involved include the normal distribution, mean ($\mu$), standard deviation ($\sigma$), probability density function, and the application of definite integrals to find cumulative probability. In terms of construction, it utilizes the GeoGebra `Integral` command to compute the area, with key objects including $\mu$, $\sigma$, $f$, $g$, $a$, and $b$ to define the distribution shape, functions, and integration boundaries. This example is suitable for high school probability and statistics, introductory college-level calculus and statistics, or data science courses, helping learners intuitively grasp the geometric meaning of the normal distribution and interval probability.