Surface Integral Calculator
Effortlessly compute surface integrals for various functions and surfaces.
Input Parameters
Enter the function to be integrated in terms of x, y, and z.
Define the surface as a vector function of parameters u and v. Use array notation [u, v, f(u,v)].
Enter the lower limits for parameters u and v, comma-separated.
Enter the upper limits for parameters u and v, comma-separated.
Result
Surface Visualization (Placeholder)
Visualization of the surface integral is a complex feature and is not implemented in this version. Future updates may include interactive 3D visualizations of the surface and function. Stay tuned!
Understanding Surface Integrals
A surface integral is a generalization of multiple integrals to integration over surfaces. Imagine you want to find the total amount of some quantity (like mass or electric charge) distributed over a curved surface. The surface integral allows you to calculate this. It extends the concept of a definite integral from curves to surfaces in space. Surface integrals are used in physics and engineering to calculate things like fluid flow through surfaces, the area of curved surfaces, and electromagnetic fields. To use this calculator, input your function, define the surface parameterization as a vector function r(u, v) = [x(u, v), y(u, v), z(u, v)], and specify the bounds for parameters u and v.
For example, to integrate f(x, y, z) = x + y + z over a surface parameterized by r(u, v) = [u, v, u*v] with bounds 0 ≤ u ≤ 1 and 0 ≤ v ≤ 1, enter 'x + y + z' as the function, '[u, v, u*v]' as the surface parameterization, and '0, 0' and '1, 1' as the lower and upper bounds respectively.