Calculus: Early Transcendentals, Chapter 6, 6.2, Section 6.2, Problem 18

You need to evaluate the volume of the solid obtained by the rotation of the region bounded by the curves y = x , y = 0, x = 2,x=4 about x = 1, using washer method, such that:
V = int_a^b (f^2(x) - g^2(x))dx, f(x)>g(x)
You may evaluate the volume
V = pi*int_2^4 (1 - y)^2dy
V = pi*int_2^4 (1 - 2 y + y^2)dy
V = pi*(int_2^4 dy - 2*int_2^4 y dy +int_2^4 y^2 dy)
V = pi*(y - 2*y^2/2 +y^3/3)|_2^4
V = pi*(y - y^2 +y^3/3)|_2^4
V = pi*(4 - 4^2 +4^3/3 - 2+ 2^2 - 2^3/3)
V = pi*(-10 + 56/3)
V = (26pi)/3
Hence, evaluating the volume of the solid obtained by the rotation of the region bounded by the curves y = x , y = 0, x = 2,x=4 about x = 1, yields V = (26pi)/3.