Homework SourseFind the volume of the solid obtained by rotating the region
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis: y=3x(x-2)^2; x=2 ; y=0 ; about the y-axis
Solution
The rotational volume of an equation or curve rotated horizontally is equal to: V = 2*pi* definite integral, from 0 to 1, of the given equation x^2/4 dx. V = 2*pi / 4 * int 0 to 1, x^2 dx V = pi / 2 * ( x^3 / 3 evaluated 0 to 1) V = pi/2 * (1^3/3 - 0^3/3) V = pi/6 = 0.5235987755983 The rotational volume of an equation or curve rotated vertically is equal to: V = 2*pi* definite integral, from 0 to 2, of the given equation x^2/4 dx. V = 2*pi / 4 * int 0 to 2, x^2 dx V = pi / 2 * ( x^3 / 3 evaluated 0 to 2) V = pi/2 * (2^3/3 - 0^3/3) V = 8pi/6 = 4pi/3 V = 4.18879020478633
