3bf408…: “As far as an amazing arc”

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Consider the region: $R=\{(x,y): 0\le x\le 2, x^3\le y\le 4x\}$ Set-up two iterated integrals that will compute the area of $R$ , one that integrates with respect to $y$ and then $x$ , and another that integrates with respect to $x$ and then $y$ . $\int _{\answer {0}}^{\answer {2}} \int _{\answer {x^3}}^{\answer {4x}} \d y \d x$ $\int _{\answer {0}}^{\answer {8}} \int _{\answer {y/4}}^{\answer {y^{1/3}}} \d x \d y$