Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

Sec. 5]_Computing th Area* of Surfaces_259
2196. A solid is bounded by the cylinder x 2
+-z 2 =a2 planes = */ 0, 2 = 0, y = x. Compute its volume.
Find the volumes bounded by the following surfaces:
2197. az = y\ x* -\-y* --='*, 2 = 0.
2198. y = y"x, f/ = 2J/T, * + 2 = 6, 2 = 0.
2199. z = x* +y\ y = x 2
, //=!, 2 = 0.
2200. x -}-*H-2 = a, 3*4-*/ = a, ~x4-tj=^a, */ = 0, 2 = 0.
2201. , + -1, y = *' = 0, 2 = 0.
2202. x 2
-h if = 2ax, 2 = a*, 2 = p* (a > p).
and the
In Problems 2203 to 2211 use polar and generalized polar
coordinates.
2203. Find the entire volume enclosed between the cylinder
x 2
-\-y 2
a 2 and the hyperboloid x 2
-f- if 2* = a 2 .
2204. Find the entire volume contained between the cone
2(* 2
+if) 2 2 = and the hyperboloid x 2
-f- if z* = a 2
.
2205. Find the volume bounded by the surfaces 2a2 = x 2
+ /* f
2
** 4-// 2 2 =a2 , 2 = 0.
2206. Determine the volume of the ellipsoid
2207. Find the volume of a solid bounded by the paraboloid
202 -= x 2
H-
2
// and the sphere * 2
4- ^ -f- 2 2 = 3a 2 . (The volume lying
inside the paraboloid is meant.)
2208. Compute the volume of a solid bounded by the jq/-plane t
the cyl inder x 2 -*y
2 = 2a^, and the cone x 2
-f if = 2 2
.
2209. Compute the volume of a solid bounded by the jq/-plane,
the surface 2 =-ae~