surface integral

A surface integral is a way to measure how a quantity, like heat, fluid flow, or magnetic field, interacts with a surface in three-dimensional space. Imagine placing a sheet of paper in a field and determining how much of that field passes through or flows across it. Instead of just summing values at points, a surface integral considers how the quantity varies across the entire surface, accounting for its shape and orientation. It’s a powerful tool used in physics and engineering to analyze interactions with surfaces, like calculating the total heat transferred through a wall or the magnetic flux through a loop.