Final answer:
The area of the region bounded by the graph can be found using integration, and in this case, the area is 0.
Step-by-step explanation:
The area of the region bounded by the graph of x = 1/2, x = 2, the x-axis, and y = 4x² - 4x² can be found using integration.
To find the bounds of integration, we need to determine the x-values where the graph intersects with the lines x = 1/2 and x = 2. Setting x = 1/2 and x = 2 equal to y = 4x² - 4x², we get 0 = 0, which means the curve intersects these lines at all x-values. Therefore, the bounds of integration are from x = 1/2 to x = 2.
The integral that represents the area is ∫(4x² - 4x²) dx from 1/2 to 2. Simplifying the integrand gives ∫(0) dx from 1/2 to 2, which is equal to 0.