010.102-2006-2-fin - 2 eK o> 2006 12 9 13r 15r 4 Z 9<...

Unformatted text preview: 2 eK o > 2006 12 9{ 13r 15r 4 Z 9 < : s2: %V IU lǣ k k( 200). M K+ c a Z @\ \ 1. (20&) 6 &` r. h h r 1 -1 1 |y| sin(1 + x2 )dxdy. 2. (20&) F+d # / r = 1 - cos (0 2)_ ?\ D M, 6 &` r. h G Q B A G / + : h r xydA. D 3. (25&) {^ R : (x - y)2 + (4y - z)2 + (z - x)2 1 \ @ # 6 &` r. h 9 / h r |x - y|dV. R a f м t 4. \" x- s9s x = a(t - sin t), Q i %%` D . t h , (a) (15&) D_ Vs\ r. (b) (15&) ' F(x, y) = (6x + ey , 4y - ln(x + 1)) D_ > D\ : (flux)\ r. h 7 x H 1 5. (25&) / S _ {" x2 + y 2 + z 2 = 1 (z 2 ) &_. / S_ >d_ z- B a a G G h B 9Ҽf r r \ . y = a(1 - cos t) (0 t 2) 6. (25&) { {/ & / S & P \ @ # 6 7" r. L G h 2 9 B < h / ` x 1 4 X -P dS = |X - P |3 1 P S_ ?\ e, / 0 P S_ \ e. @ S 7. (25&) / S\ " z = 1 - x2 + y 2 z 0 s /_ n k 0 # G h B r B G r Q 7 . ' F(x, y, z) = (x + y 2 z, y + ex , x2 + y 2 + z) S\ 4 ` r. R H 8. # 7' Q F(x, y, z) = / 9 \ @ # 6 |\ r. , r = H (a) (15&) F_ curl F\ r. h r / h G / (b) (15&) B S : (x - 1)2 + (y - 2)2 + z 2 = 1 (z 0)\ @ # curl F dS S r(x2 yz -xz , ,0 2 ) r(x2 + y 2 ) +y x2 + y 2 + z 2 . \ r. , S_ n k 0 2 &. r & ...
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