Calculus: Early Transcendentals, Chapter 6, 6.2, Section 6.2, Problem 5

You need to evaluate the volume of the solid obtained by the rotation of the region bounded by the curves x = 2sqrt y, x =0 , the line y = 9, 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 = 9 is given. The other endpoint can be evaluated by solving the following equation:
2sqrt y = 0 => 4y = 0 => y = 0
You may evaluate the volume
V = pi*int_0^9 ((2sqrt y)^2)dy
V = pi*int_0^9 (4y)dy
V = 4pi*y^2/2|_0^9
V = 2pi*y^2|_0^9
V = 2pi*(9^2 - 0^2)
V = 2pi*(81)
V = 162pi
Hence, evaluating the volume of the solid obtained by the rotation of the region bounded by the curves x = 2sqrt y, x =0 , the line y = 9, about y axis, yields V = 162pi .