Calculus: Early Transcendentals, Chapter 6, 6.2, Section 6.2, Problem 2

You need to evaluate the volume of the solid obtained by the rotation of the region bounded by the curves y = 1 - x^2 , y = 0 , about x 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 endpoints, hence you need to solve the following equation:
1 - x^2 = 0 => x^2 - 1 = 0 => (x-1)(x+1) = 0 => x = 1, x = -1
You may evaluate the volume
V = pi*int_(-1)^1 (1 - x^2)^2dx
V = pi*int_(-1)^1 (1 - 2x^2 + x^4)dx
V = pi*(int_(-1)^1 dx - 2*int_(-1)^1 x^2 dx + int_(-1)^1 x^4 dx)
V = pi*(x - 2x^3/3 + x^5/5)|_(-1)^1
V = pi*(1 - 2*1^3/3 + 1^5/5 - (-1) + 2*((-1)^3)/3 - ((-1)^5)/5)
V = pi*(1 - 2/3 + 1/5 + 1 - 2/3 + 1/5)
V = pi*(2 - 4/3 + 2/5)
V = pi*(30 - 20 + 6)/15
V = (16pi)/15
Hence, evaluating the volume of the solid obtained by the rotation of the region bounded by the curves y = 1 - x^2 , y = 0 , about x axis, yields V = (16pi)/15.