Find the volume of the solid whose base is the region in the xy-plane that is bounded by the parabola y = 4 - x^2 and the line y = -3x, while the top of the solid is bounded by the plane z = x + 5. The volume is units^3. (Type an integer or a simplified fraction.)
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The region R is bounded by the parabola y = 4 - x^2 and the line y = 3x. So, the integral setup is: \[ \int_{-1}^{4} \int_{-3x}^{4-x^2} (x + 5) \, dy \, dx \] Show more…
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