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

266 Multifile and Lire Integrals [Ch. 7
2240. V is a tetrahedron bounded by the planes
X J r yJrZ =\, X = 0, J/ = 0, 2 = 0.
2241. V is a cylinder bounded by the surfaces
JC' + ^fl 1
, 2 = 0, 2 = /f.
2242*. V is a cone bounded by the surfaces
2243. V is a volume bounded by the surfaces
Compute the following integrals:
2244.
000
2 2 V
2245. djt
J
dy
* + +-2+1
2246 .
a
I fd*
.) .1 00
1 1-X
rfy ('
J
1-JC-t/
2247.
] dx J dy J xyzdz.
p o o
2248. Evaluate
J
d* dy dz
1)3 '
where V is the region ol integration bounded by
planes and the plane x-\~y-[z\.
2249. Evaluate
r r r
(V}
the coordinate
where V (the region of integration) is the common part
paiaboloid 2cu^x 2 2
-\-y and the sphere X? + y* + 2 2
2250. Evaluate
(V)
^3a 2 .
of the
where V (region of integration) is the common part of the
spheres x2 + y* \-z* ^R' and x 2
+ \f + z 2 ^ 2Rz