Question

How do you determine the area of the region between the curves y = 4x² - x³ and y = x² - 3x?

a) By evaluating the definite integral of the difference between the curves
b) By finding the indefinite integral of each curve
c) Using the midpoint rule
d) Utilizing Riemann sums

Answer 1

The correct answer is option a. To determine the area of the region between the curves y = 4x² - x³ and y = x² - 3x, we can use the method of evaluating the definite integral of the difference between the curves.

Step-by-step explanation:

To determine the area of the region between the curves y = 4x² - x³ and y = x² - 3x, we can use the method of evaluating the definite integral of the difference between the curves. This is because the area between two curves can be found by subtracting the value of one curve from the other and integrating it over the given interval.

The definite integral is denoted as ∫ab (f(x) - g(x)) dx, where f(x) and g(x) are the given functions, and a and b are the limits of the interval over which we want to find the area. By evaluating this definite integral, we can determine the area of the region between the curves.

Therefore, option a) By evaluating the definite integral of the difference between the curves is the correct option.