Calculus: Early Transcendentals, Chapter 6, 6.2, Section 6.2, Problem 1

The volume of the solid obtained by rotating the region bounded by the curves y=2 - x/2, y=0, x=1,x=2 , about x axis, can be evaluated using the washer method, such that:
V = int_a^b pi*(f^2(x) - g^2(x))dx
Since the problem provides you the endpoints x=1,x=2, you may find the volume such that:
V = int_1^2 pi*(2 - x/2 - 0)^2 dx
V = pi*int_1^2 (2 - x/2)^2dx
V = pi*int_1^2 (4 - 2x + x^2/4)dx
V = pi*(int_1^2 dx - 2int_1^2 x dx + (1/4)int_1^2 x^2 dx)
V = pi*(x - x^2 + x^3/12)|_1^2
V = pi*(-2 + 2^2 - 2^3/12 - 1 + 1^2 + 1^3/12)
V = pi*(2 - 8/12 + 1/12)
V = (17pi)/12
Hence, evaluating the volume of the solid obtained by rotating the region bounded by the curves y=2 - x/2, y=0, x=1,x=2 , about x axis , using the washer method, yields V = (17pi)/12.