Final answer:
The area under a curve can be determined by dividing the interval into n equal subintervals and calculating the area of a circumscribed polygon, relating to Riemann sums or, in some cases, by using the integral of the function.
Step-by-step explanation:
The area under a curve of a function on a stated interval can be approximated by dividing the interval into n equal subintervals and finding the area of the circumscribed polygon. This method is closely related to the concept of Riemann sums where the areas of shapes such as rectangles or trapezoids are summed to approximate the total area under a curve.
To perform this calculation, one approach is to calculate the area of individual shapes (e.g., triangles, rectangles) based on the graph of the function. For example, if the curve represents a straight line, the area of a right triangle or rectangle can be calculated using the base and height. If the graph represents a cumulative distribution function, the area under the curve corresponds to the probability for a given interval, and the total area under the curve and above the x-axis represents a total probability of one. The mentioned references to rectangles and triangles in the task imply a linear function or a function that can be approximated by linear segments over small intervals.
In the case of non-linear functions, the concept of an integral is pertinent as the limit of the sum of infinitely small rectangles. The area under the curve of a force versus displacement graph, for instance, represents work done and can be calculated using the integral of that function over the specified interval.