Calculus: Early Transcendentals, Chapter 6, 6.2, Section 6.2, Problem 15

You need to evaluate the volume of the solid obtained by the rotation of the region bounded by the curves y = x^3 , y = 0, x = 1 , about x = 2, using washer method, such that:
V = int_a^b (f^2(x) - g^2(x))dx, f(x)>g(x)
You need to find one endpoint, hence you need to solve the following equation:
x^3 = 0=> x = 0
You may evaluate the volume
V = pi*int_0^1 (2 - root(3) y)^2dy
V = pi*int_0^1 (4 - 4 root(3) y + root(3) (y^2))dy
V = pi*(int_0^1 4dy - 4*int_0^1 y^(1/3)dy + int_0^1 y^(2/3) dy)
V = pi*(4y - 4*(3/4)*y^(4/3) + (3/5) y^(5/3))|_0^1
V = pi*(4y - 3*y^(4/3) + (3/5) y^(5/3))|_0^1
V = pi*(4 - 3 + (3/5) )
V = pi*(1 + 3/5)
V = (8pi)/5
Hence, evaluating the volume of the solid obtained by the rotation of the region bounded by the curves y = x^3 , y = 0, x = 1 , about x = 2, yields V = (8pi)/5 .