用极坐标计算二重积分教学初探

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1、用极坐标计算二重积分教学初探25???T1?)<?<?<?<?<?<?<?<?<?<?<?<?<?<?<??g?????G?v?????;????2009??3?oVol.25No.1<?<?<?<?<?<?<?<?<?<?<?<?<?<?JournalofLvliangHigherCollegeMar.2009?]?????V??????

2、?????3?????7?????t??(???????????????3???N??,????????710061)??<???:????:,?]?????V???????????3:7???????????.???)???v?????????+???p,????????.?x?]?????V???N?????????G???????3???[?],?a?r???????p?????????????????????n.???c??:?????V;?????3;???????V???=???3????:O

3、171<?<????c?V???2:A<?<??????H??:1008-7834(2009)01-0009-031<?????????????[1]?T???U?????T?????T237???=???<:?????3?p???s?3?H?3?????????3,?H?9?????????????n?pf(x2+y2)??,???]?????V????T:T:x=rcos1?,y=rsin1?,<?0O?r<+O6,0O?1?O?21?,?????????&l

4、t;???H???3?p???H??????????????.?.????????r??1????1?????/0O?r<+O6,0O?1?O?21?,?b???s?p????????T???????c[1]???321.13,?w????r??1????1?????/,?v?????)?????p???8???????1?????k?????????V?H?1?????V?=???0???????1???????/,1????1???????s[0,21?]?W???????+?p??[1?,1?],?

5、?[1?,1?]Α[0,21?],?X?????U?a?i?v?C.2<??????R?]?f???l???M???????3????,???E?]?????V???n?????????3????,?X???3?p?????E?]?????V???N???p,?]????????(r,1?)???1?????M???????N?8??????.????1.??1<??????3OyOyD<?f(x,y)d1??H?a?????V???n?????;???3,???=???3?p??D?p{(x

6、,y)

7、x2+y2O?2x}.??:?f???q?3?????3?p??D={(x,y)

8、x2+y2O?2x},????,??1?

9、???p???3?p??D?]???????V???N??????,??2?=?

10、???p???3?p??D?]?????V???N??????.????A:???)?1???<1????1???????s[0,21?]?W???????+?p??[1?,1?]???????3?p???????[,?3???3?p??D={(x,y)

11、x2+y2O?2x}?3?a?8???3

12、???????????V???????nD=D1+D2={(r,1?)

13、0O?rO?2cos1?,0O?1?O?1?/2}+{(r,1?)

14、0O?rO?2cos1?,31?/2O?1?O?21?},?R???lOyOyD<?f(x,y)d1?=Oy01?/2d1?Oy02cos1?f(rcos1?,rsin1?)rdr+Oy31?/221?Oy02cos1?f(rcos1?,rsin1?)rdr.(1)<?<?????B:OyOyD<?f(x,y)d1?=Oy-1?/21?/2d1?Oy

15、02cos1?f(rcos1?,rsin1?)rdr(2)3226???9???????t??(2),??,?G??,?????

16、????,???????????????3???N?????o9:2008102:1979.[1?,1?]Α[0,21?]?????p,?u?????????)???1??,?????p????B?u????,?i?)???1?????]?3???????f