4) Region R is bounded by the graphs of $y = x^3$ and $y = \sqrt{x}$ in the first quadrant. Find the area of R by establishing a double integral for the area.
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$x^3 = \sqrt{x}$ $x^6 = x$ $x^6 - x = 0$ $x(x^5 - 1) = 0$ $x = 0$ or $x^5 = 1$, so $x = 1$. The points of intersection are $(0, 0)$ and $(1, 1)$. Show more…
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