Surfaces in three-dimensional space can be represented through explicit, parametric and implicit equations, which describe the relationship between the variables x, y and z. Graphs of linear equations produce flat planes, while quadratic equations form objects such as spheres or ellipsoids. In this research, a theoretical approach is combined with interactive visualization to analyze various surface shapes. Through the use of GeoGebra software, this analysis makes it easier to understand surface orientation and shape, such as normal vectors and curvature, as well as applications in vector fields. This research also investigates the concepts of Cartesian coordinates in three-dimensional space, by depicting surfaces in the form of graphs of functions of two variables. It is hoped that the results of this research can provide deeper insight into the geometric properties of surfaces and how to visualize them effectively in mathematics and physics applications.

Numerical integration is a method used to calculate the integral of functions that cannot be integrated analytically. Several methods that are often used in numerical integration include that Simpson 1/3 method, Simpson 3/8 method, and the Trapezoidal method. This research aims to apply and compare the accuracy and efficiency of the third method in solving various types of integral functions using computing software. With the help of software such as MATLAB and Python, the precision of the results obtained from each method is analyzed and compared with analytical solutions (if available) or approximate integral value estimates. The results show that the Simpson 3/8 method tends to be more accurate for more complex functions than the Simpson 1/3 and Trapezoid method. However, the Trapezoidal method has advantages in computational speed and algorithm simplicity. This study provides important insights for computing software users in selecting appropriate numerical integration methods based on function complexity and accuracy requirements.