Provide an Appropriate Response $f ( x ) = \frac { 1 } { x ^ { 2 } } , x \geq 1$

Essay

Provide an appropriate response.
-Let $f ( x ) = \frac { 1 } { x ^ { 2 } } , x \geq 1$
(a) Find the area of the region between the graph of $y = f ( x )$ and the $x$ -axis.
(b) If the region described in part (a) is revolved about the x-axis, what is the volume of the solid that is generated?
(c) A surface is generated by revolving the graph of $y = f ( x )$ about the $x$ -axis. Write an integral expression for the surface area and show that the integral converges.
(d) Use numerical techniques to estimate the area of the region in part (c), to an accuracy of at least two decimal places.