The function is ,
,
and
.
(a)
\Find volume of the solid about - axis.
Solve the function in terms of .
Find the point of intersections.
\ and
.
Point of intersection is .
and
.
Point of intersection is .
By usig shell method
Integrate with to
.
Power rule of integral: .
The volume of the curve about -axis is
cubic-units.
(b)
\Find volume of the solid about -axis.
Solve the function in terms of .
Integrate with to
.
.
The volume of the curve about -axis is
cubic units.
(c)
\Find volume of the solid about the line .
Solve the function in terms of .
The radius of the curve is .
The height of the curve is .
By usig shell method.
\Integrate with to
.
Power rule of integral is
The volume of the curve is cubic units.
(a) The volume of the curve about -axis is
cubic units.
(b) The volume of the curve about -axis is
cubic units..
(c) The volume of the curve is cubic units.