Consider a region R bounded by the functions f(x) = x2 + 1 and g(x) = x over the interval [0, 2]. (a) Draw an accurate graph of the region R. (b) Find the area of the region. (c) A solid of revolution is obtained by revolving a plane region bounded by a curve f(x), x ∈ [a, b], about x-axis. The volume of such solid is as V = π∫a b [f(x)]2 dx. Calculate the volume of the solid generated by the region R revolving about the x-axis.
![Consider a region R bounded by the functions f(x) = x2 + 1 and g(x) = x over the interval [0, 2]. (a) Draw an accurate graph of the region R. (b) Find the area of the region. (c) A solid of revolution is obtained by revolving a plane region bounded by a curve f(x), x ∈ [a, b], about x-axis. The volume of such solid is as V = π∫a b [f(x)]2 dx. Calculate the volume of the solid generated by the region R revolving about the x-axis.](https://www.doubtrix.com/uploads/editor/1782620418zjZNPxKVjz.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 ∫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)
