Final answer:
The area under the function y = 20x - x^2 is approximated by dividing the area into an indefinitely large number of rectangles, making the option c. the correct choice. This process relates to calculating the definite integral through Riemann sums in integral calculus.
Step-by-step explanation:
To approximate the area under the curve y = 20x - x^2, the method often used is division into rectangles. The option that correctly describes this method is c. The area is divided into rectangles, and their number becomes arbitrarily large (tends to infinity). This is a fundamental concept in integral calculus known as the Riemann sum, where the area under a curve is approximated by summing the areas of multiple rectangles. As the number of rectangles increases (their width decreases), the approximation becomes more precise, ideally reaching the true area in the limit as the number of rectangles approaches infinity.
When the number of rectangles increases without bound, the total area of these rectangles approaches the exact area under the curve, which is also known as the definite integral of the function between two points. This process does not usually involve a fixed number of rectangles for approximation, since an increase in the number of rectangles enhances accuracy. In more advanced applications, different methods like the trapezoidal rule or Simpson's rule might be used to get better approximations with fewer shapes.