Integral Setup for Bounded Region Between Curves y4x and yx3

Set up a generic integral for the region bounded by the curves $y = 4x$ and $y = x^3$, using the order of iteration $dy/dx$.

Setting up an integral to find the area between two curves involves understanding the region you are working with and choosing the correct bounds and order of integration. Here, you are asked to set up the integral with respect to y first, followed by x, meaning you must view the problem in vertical slices. This approach requires determining where these vertical slices begin and end, which often involves solving for points of intersection between the curves to determine the limits of integration. Conceptually, this changes how you consider the roles of the functions: each slice extends from the lower function to the upper function.

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