Define R as the region bounded by the graphs of f(x) = 3x – x^2 and the x-axis. Which of the following represents the volume of the solid of revolution formed by rotating R about the y-axis? ∫0 3 π(3x^3 – x^4 )dx ∫0 3 2π(3x – x^2 )dx ∫0 3 2πxdx ∫0 3 2π(3x^2 – x^3 )dx ∫3 0 2π(3x^2 – x^3 )dx
![Define R as the region bounded by the graphs of f(x) = 3√x and g(x) = x^2 / 4 over the interval [1, 4]. Which of the following represents the volume of the solid of revolution formed by rotating R about the line x = -1 ∫1 4 2π(x + 1) (3√x – x^2 / 4 ) dx ○ ∫1 4 2π(x - 1) ( x^2 / 4 - 3√x) dx ∫1 4 2π(x - 1) (3√x – x^2 / 4 ) dx ∫1 4 2π(x + 1) ( x^2 / 4 - 3√x) dx ∫4 1 2π(x + 1) (3√x – x^2 / 4 ) dx](https://www.doubtrix.com/uploads/editor/5896888824LCQVfAnVrd.png)
![Define R as the region bounded by the graphs of f(x) = 3√x and g(x) = x^2/4 over the interval [1, 4]. Which of the following represents the volume of the solid of revolution formed by rotating R about the line x = -1?](https://www.doubtrix.com/js/ckeditor/filemanager/connectors/php/editor/1701968112-Jzfvgrogmd.png)
