The Concept:
Normally, when calculating the area (2-dimensional) under a curve, we take thin, rectangular slices, get each’s specific height (1-dimensional) with , then add them all up (using integration).
But (one of) the beautiful thing(s) about Calculus? It’s not limited to 2 dimensions. If I wanted to calculate the volume of a shape (3-dimensional), I’d follow the exact same method. I’d cut the shape (3D) into thin planes (2D), get each of their areas (2D again), then add all those up with integration again.
The only thing extra step is you have to work on getting a formula for the area of the plane at any point x (as opposed to the typical area of a function). It’s really quite a neat discovery.