Final answer:
To find the area of the region bounded between the curves y = 2x^3, y = 2x, and the y-axis, set up the integral with the limits of integration and evaluate.
Step-by-step explanation:
To find the area of the region bounded between the curves y = 2x^3, y = 2x, and the y-axis, we need to determine the limits of integration and set up the integral.
The limits of integration can be found by determining the x-values where the curves intersect. Setting the two curves equal to each other, we have 2x^3 = 2x. Solving this equation, we find that x = 0 and x = 1. So our limits of integration are 0 and 1.
The integral to find the area is given by A = ∫(2x - 2x^3)dx, where the lower limit is 0 and the upper limit is 1. Evaluating this integral, we find that the area is 1/2 square units.