Calculus: Early Transcendentals, Chapter 6, 6.2, Section 6.2, Problem 3

The volume of the solid obtained by rotating the region bounded by the curves y=sqrt(x-1), y=0, x= 5 , 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 endpoint x = 5, you need to find the other endpoint of interval, hence, you need to solve for x the following equation, such that:
sqrt (x-1) = 0 => x - 1 = 0 => x = 1
V = int_1^5 pi*(sqrt(x-1) - 0)^2 dx
V = pi*int_1^5 (x - 1)dx
V = pi*int_1^5 (x)dx - pi*int_1^5 dx
V = (pi*x^2/2 - pi*x)|_1^5
V = (pi*5^2/2 - pi*5 - pi*1^2/2 + pi*1)
V = (25pi)/2 - pi/2 - 4pi
V = 12pi - 4pi
V = 8pi
Hence, evaluating the volume of the solid obtained by rotating the region bounded by the curves y=sqrt(x-1), y=0, x= 5 , about x axis , using the washer method, yields V = 8pi.