The figure above shows the graph of the equation $x ^ { \frac { 1 } { 2 } } + y ^ { \frac { 1 } { 2 } } = 2$. Let R be the shaded region between the graph of $x ^ { \frac { 1 } { 2 } } + y ^ { \frac { 1 } { 2 } } = 2$ and the $X$-axis from $x = 0$ to $x = 1$. (a) Find the area of R by setting up and integrating a definite integral. (b) Set up, but do not integrate, an integral expression in terms of a single variable for the volume of the solid formed by revolving the region R about the $X$-axis. (c) Set up, but do not integrate, an integral expression in terms of a single variable for the volume of the solid formed by revolving the region R about the line $x = 1$.