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

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gee. 7]_Tr<strong>ipl</strong>e Integrals_267<br />

2251. Evaluate<br />

^zdxdydz,<br />

(V)<br />

where V is a volume bounded by the plane z = and the upper<br />

half of the ellipsoid -+ j. + -J.==l.<br />

2252. Evaluate<br />

(V)<br />

where V is the <strong>in</strong>terior of the ellipsoid ~^r + "^r<br />

2253. Evaluate<br />

where V (the region of <strong>in</strong>tegration) is bounded by<br />

2 2 2 = (jc<br />

2<br />

hi/ and the ) plane z = h.<br />

2254. Pass<strong>in</strong>g to cyl<strong>in</strong>drical coord<strong>in</strong>ates, evaluate<br />

X z<br />

2<br />

IJ<br />

the cone.<br />

where V is a region bounded by the surfaces x* +y* -\- z* = 2Rz 9<br />

2<br />

jc -|<br />

2<br />

// -=z a<br />

and conta<strong>in</strong><strong>in</strong>g the po<strong>in</strong>t (0,0, R).<br />

2255. Evaluate<br />

2 J 21 - jc j a<br />

first transform<strong>in</strong>g it to cyl<strong>in</strong>drical coord<strong>in</strong>ates.<br />

225(5. Evaluate<br />

- - -<br />

di/ J dz,<br />

first transform<strong>in</strong>g it to cyl<strong>in</strong>drical coord<strong>in</strong>ates.<br />

2257. Evaluate<br />

R VR*-X* Vfla-jir*-0a<br />

\dx \ dy J<br />

J<br />

(A:<br />

-/? -/f^TJa o<br />

first transform<strong>in</strong>g it to spherical coord<strong>in</strong>ates.<br />

+

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