MathDB

Let

K

be the figure bounded by the graph of function y \equal{} \frac {x}{\sqrt {1 \minus{} x^2}},

x

axis and the line x \equal{} \frac {1}{2}. (1) Find the volume

V_1

of the solid generated by rotation of

K

around

x

axis. (2) Find the volume

V_2

of the solid generated by rotation of

K

around

y

axis. Please solve question (2) without using the shell method for Japanese High School Students those who don't learn it.

Problem Statement