Volume of a solid by revolving the regio bounded by y=sq root of x, the x-axis, x=0, x=2 around the y-axis?

Question

Volume of a solid by revolving the regio bounded by y=sq root of x, the x-axis, x=0, x=2 around the y-axis?

Answer 1

y = √x

y(2) = √2

Transforming variables,

x = y^2

Using the disc method,

dV = π(2^2 - x^2)dy

dV = π(4 - y^4)dy

V = π(4y - (1/5)y^5) from 0 to √2

V = π(4 - (1/5)y^4)y from 0 to √2

V = π(4 - 4/5)√2

V ≈ 14.21723 ≈ 14.2