Calculus: Early Transcendentals, Chapter 6, 6.2, Section 6.2, Problem 10

You need to evaluate the volume of the solid obtained by the rotation of the region bounded by the curves y = (1/4)x^2 , x =2 , the line y = 0, about y axis, using washer method, such that:
V = int_a^b (f^2(x) - g^2(x))dx, f(x)>g(x)
You need to find the next endpoint, since one of them, y = 0 is given. The other endpoint can be evaluated by solving the following equation:
2sqrt y = 2 => sqrt y = 1 => y = 1
You may evaluate the volume
V = pi*int_0^1 (2^2 - (2sqrt y)^2)dy
V = pi*int_0^1 (4 - 4y)dy
V = 4pi*int_0^1 (1 - y)dy
V = 4pi*(int_0^1 dy - int_0^1 ydy)|_0^1
V = 4pi*(y - y^2/2)|_0^1
V = (4pi*y - 2pi*y^2)|_0^1
V = (4pi*1 - 2pi*1^2 - 4pi*0 + 2pi*0^2)
V = 2pi
Hence, evaluating the volume of the solid obtained by the rotation of the region bounded by the curves y = (1/4)x^2 , x =2, y=0 , about y axis, yields V = 2pi.