Line, surface, and volume integrals are all tools from calculus used to integrate functions over one, two, or three dimensions, respectively. They help us calculate quantities like total work done, flux across a surface, or the mass of an object with varying density. 

Integrate a scalar field (temperature) or a vector field (force) along a curve

Imagine dividing the curve into tiny segments, multiplying the function's value at each segment by the segment's length and direction, and summing up.

Applications: calculating work done by a force along a path, finding circulation in a fluid flow.

Integrate a function over a two-dimensional surface

Similar to a line integral, but instead of a curve, you're summing the function's value over tiny surface elements, considering their area and orientation

Applications: finding flux (rate of flow) across a surface, calculating surface area with a density function

Integrate a function over a three-dimensional solid region

Imagine dividing the solid into tiny boxes, multiplying the function's value at each box by its volume, and summing everything up

Applications: calculating the total mass of an object with varying density, finding the average temperature within a region.