What does the geometric interpretation of integration signify?

The geometric interpretation of integration is fundamentally related to calculating areas under curves. When you visualize the graph of a function, integration allows you to quantify the area between the curve defined by the function and the x-axis, over a specified interval. This area can represent various physical quantities depending on the context; for example, it can represent distance traveled when the function represents velocity over time, or it can represent total accumulated quantity when the function models a varying rate.

In a practical sense, integration sums up an infinite number of infinitesimally small rectangles under the curve, each with a width approaching zero, effectively giving you the total area. This is why integration is often referred to as the reverse process of differentiation, which deals with slopes and rates of change rather than areas.

The other options pertain to different aspects of calculus. Finding slopes of curves relates to differentiation, which measures how a function changes at a particular point. Determining rates of change also ties into differentiation, as it focuses on how a function's output changes with respect to its input. Identifying points of intersection generally involves solving equations or systems, which is a different process not directly connected to the geometric interpretation of integration.