Final answer:
The area of the region in quadrant I bounded by y = 2x² and y = 2x³ can be found by evaluating the integral ∫(2x³ - 2x²) dx from 0 to 1.
Step-by-step explanation:
To find the area of the region in quadrant I bounded by y = 2x² and y = 2x³, we need to determine the limits of integration and set up the integral. The curves intersect when 2x² = 2x³, which simplifies to x² = x³. Solving for x, we find that x = 0 and x = 1.
The correct integral to find the area is ∫(2x³ - 2x²) dx from 0 to 1, which is option A. Evaluating this integral will give you the area of the region in quadrant I bounded by the curves.