南京邮电大学 《高等数学》(下册) 习题参考答案
第七章 习题7.1 2.(1)
??(x?y)D?12d????(x?y)3d?; (2)
D??(x?y)D3d????(x?y)2d?;
D (3)
???xyzdv????xyzdv;
?(4)
???(x?2?y2?z2)2dv????(x2?y2?z2)dv;
?33. (1)0?I??2; (2)36??I?100?; (3)?32??I?323?;
33习题7.2
1.(1)
r?040dx?2x0f(x,y)dy或?r040dy?y2f(x,y)dx;
4?y(2)
?dx??rr2?x2f(x,y)dyx或或1?1?x24?x2?dy?12r2?y2?r2?y22f(x,y)dx;
22(3)
?21dx?1f(x,y)dyx4?x2?1dy?1f(x,y)dx??dy?f(x,y)dx;
y1y(4)??1dx?1?x2f(x,y)dy???1dx??24?y2?14?y21f(x,y)dy???1?2dx?4?x2?4?x2f(x,y)dy??dx?124?x2?4?x2f(x,y)dy或
?1dy??4?y2f(x,y)dx??dy??2?4?y2f(x,y)dx??1?1dy??1?y2?4?y2f(x,y)dx??1?1dy?4?y2.1?y2f(x,y)dx.
2.(1)
?dx?011xf(x,y)dy; (2)
?dx?04xx2f(x,y)dy;
(3)
?dx??111?x20ef(x,y)dy; (4)
?1?1dy?y?12y?12f(x,y)dx;
1 (5) 3.(1)
?10dy?yf(x,y)dx; (6)
e?0?1dy???2arcsinyf(x,y)dx??dy?0??arcsinyarcsinyf(x,y)dx.
203?69?; (2)?; (3); (4)e?e?1; (5); (6)?1. 325542?717. 5. . 6. . 4. 3269.(1)
?2?0d??f(?cos?,?sin?)?d?; (2)
ab???d??2?22cos?0f(?cos?,?sin?)?d?;
(3)
?1?20d??(cos??sin?)?10f(?cos?,?sin?)?d?.
?10.(1)
?40d???3sec??0f(?cos?,?sin?)?d????2d??42sec?csc?0f(?cos?,?sin?)?d?;
1? (2)
??d??40f(?)?d?; (3)
?20d??(cos??sin?)?1f(?cos?,?sin?)?d?;
? (4)
?40d??sec?sec?tan?f(?cos?,?sin?)?d?.
3?22?1; (3) ?(e?1); (4) .
6443?411.(1) a; (2)
412.(1) 2?13.
?22; (2)
?8(??2); (3) 14a4; (4)
2?(b3?a3). 3?4a2.
2?. 37e?1115. (1) ln2; (2) ; (3) ?ab.
32214.(1)6?; (2) 16.(1)提示:作变换?习题7.3 1.(1) (3)
?u?x?y?u?x; (2)提示:作变换?.
?v?y?x?v?x?y1?dx??11x11?x2?1?x2x2?y2dy?2x?y2f(x,y,z)dz; (2)
?dx??11?x011?x2?1?x2xydy?22?x2x?2y2f(x,y,z)dz;
?1?1dx?2dy?0f(x,y,z)dz; (4)
?10dx?dy?f(x,y,z)dz.
02. (1)
115?; (2) (ln2?); (3) 0; (4) h2R2; (5) 364284?2?.
1716; (2) ?; (3) ?. 812347445. (1) ?; (2) ?a; (3) ?(A5?a5).
56154. (1)
6.直角坐标系 柱面坐标系
?dx??111?x2?1?x2dy??2?x2?y2x2?y2f(x,y,z)dz;
?2?0d??d??02?12??2f(?cos?,?sin?,z)?dz;
f(rsin?cos?,rsin?sin?,rcos?)r2sin?dr.
? 球面坐标系 7.(1)
?0d??d??402032?3?2; (2) ?a3; (3) ; (4) ?(55?4). 3263
南京邮电大学-高数书上的习题标准答案(下册)
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