发布时间 : 星期三 文章高等数学A(下)复习题(同济第六版)更新完毕开始阅读
A.2??rf(r)dr B. 4??rf(r)dr C. 2??001110f(r)dr D. 4??rf(r)dr
02r37.设积分区域D?{(x,y)|x2?y2?1,x?0,y?0},则 A. 2? B. ? C. 38.设D是矩形域 0?x???d?=( )。
D?? D. 24π,?1?y?1,则??xcos(2xy)dxdy的值为( ). 4DA. 0 B. ?111 C. D. 24239、设积分区域D是圆环1?x2?y2?4 ,则二重积分A.C.
??Dx2?y2dxdy?( )
?? 2? 0 2? d?? r2dr B.? 1 4 2? 0 2? d?? r dr
1 4 0 d?? rdr D.? 1 22 0 d?? r dr
1 240.设I1???(x?y)D2其中D?{(x,y)|(x?2)2?(y?1)2?1},d?,I2???(x?y)3d?,
D则( )
A.I1?I2 B.I1?I2 C. I1?I2 D. 无法比较
2241. 设D:x?y?1,则?ye??xdxdy=( ). D2A. ?(1?e) B. ?(1?) C. 0 D. ?(1?) 42.设D由x?0,y?1,y?x围成,则
A.D.
1e1e??f(x,y)dxdy?( )
D? 1 0 1 0 ydy?f(x,y)dx 0 1 B.
? 1?x 1 0dx?f(x,y)dy 0 x C.
? 1 0dy?f(x,y)dx
y 1?dy?f(x,y)dx
043. 交换二次积分顺序后, A. C.
? 1 0 dx? 0 f(x,y)dy=( )。
1 1 ?x 0 0 1?y? 1 0 dy? f(x,y)dx B. ? dy? 0 1 f(x,y)dx f(x,y)dx
dxdydz化为三次积22????x?y?1? 1- x 0 dy? f(x,y)dx D. ? dy? 0 0 1 1 02244. 设?是平面z?1与旋转抛物面x?y?z所围区域,则
分等于( ) A.
? 2? 0d?? 1 2? 1 1rrdrdzd?dr B.? r2? 0? r21?r2? 0dz 01?r2 1
? 1 1 1rrdr?2dz D.?d??2dr?dz C.?d?? 0 01?r2 r ?? r1?r2 045.设f(x,y)连续,且 f(x,y)?xy???f(u,v)dudv,其中D是由y?0,y?x2,x?1 ? 1D所围区域,则f(x,y)= ( ) A. xy B. 2xy C. xy?1 D. xy?1 846.设f(x,y)在D:x2?y2?1,y?0连续,则A.
??f(x,y)d??( )
D 1-x2 0 1?x21?x2? 2? 0d??f(rcos?,rsin?)rdr B. ?dx? 0 1 1 0 1f(x,y)dy
f(x,y)dy
C.
? ? 0d??f(rcos?,rsin?)rdr D. ? ?1dx? ? 0 147.若区域D为(x,y)|x?1,y?1,则
-1
????xeDDcos(xy)。 sin(xy)dxdy=( )
A. e B. e C. 0 D. π 48. 设D由x?0,y?1,y?x围成,则 A.
C.
??f(x,y)dxdy?( ).
1 x 0 0? 1 0dy?f(x,y)dx B. ?dx?f(x,y)dy
0 1? 1 0dy?f(x,y)dx D. ?dy?f(x,y)dx
y 0 0 1 1 y49.设f(x,y)为连续函数,则积分
?dx?01x20f(x,y)dy??dx?11x222?x0f(x,y)dy
22?x可交换积分次序为( ) A.C.
?101dy?f(x,y)dx??dy?01y22?y0f(x,y)dx B. ?dy?f(x,y)dx??dy?00112?x0x0f(x,y)dx
?0dy?2?yyf(x,y)dx D. ?dy?2f(x,y)dx
50. 交换二次积分顺序后,A.C.
? 1 0 dx? 1?x 0 f(x,y)dy=( )
1 1 ?x 0 0? 1 0 dy? f(x,y)dx B.? dy? 0 1 1 0 0 1 f(x,y)dx f(x,y)dx
? 1- x 0 dy? f(x,y)dx D.? dy? 1?y 051.在公式
?f(?,?)????f(x,y)d??lim?D?0iii?1?(xe??D2ni中?是指( )
A.最大小区间长度 B.小区域最大面积 C.小区域直径 D.小区域最大直径
2252. 设D:x?y?1,则?y2)dxdy=( ).
A. ?(1?e) B. ?(1?) C. ?(e?1) D. ?(1?)
1e1e
x2y2253.设L表示椭圆2?2?1,方向逆时针,则?(x?y)dx?( )
LabA.πab B.-πab C.a?b D. 0 54. 设L是y=4x从(0,0)到(1,2)的一段,则
22
22?yds?( )
LA.
?0x1?4xdx B. ?22011y2x2y1?dy C. ?x1?dx D. ?1?4y2dy
004455. 设L是从点A(1,0)到点B(-1,2)的弧段,则曲线积分 A.2 B.22 C.2 D.0
222256. 设?为球面x?y?z?a(a?0),则
? L(x?y)ds=( )
1dS的值为( )。 ??222x?y?z?4πa D. 4π 322257. 设S是球面x2?y2?z2?R2,则曲面积分??(x?y?z)dS? ( )
A. 2π B. 3π C.
SA. ?R B. 2?R C. 4?R D. 6?R 58. 设L是从点(0,0)到点(2,1)的直线段,则
4444? L2yds? ( )。
A. 5 B.
510 C. 10 D. 2259.用格林公式求由曲线C所围成区域D的面积A,则A=( )
A. C.
?Cxdy?ydx
B. D.
?Cydx?xdy
1xdy?ydx 2?CL1ydx?xdy 2?C60.已知曲线积分
?F(x,y)(ydx?xdy)与积分路径无关,则F(x,y)必满足条件( )
A. xFy?yFx B. xFy?yFx?0 C. xFx?yFy D. xFx?yFy 61. 设L为连接(1,0)及(0,1)两点的直线段,则
?(x?y)ds?( ).
LA. 2 B. 1 C. 2 D. 3 62. 设L为从点A(1,1)到点B(1,0)的直线,则下列等式正确的是( ) A.
11 xdx?1 xdy?1 yds?? ydy?? B. C. D. ??? L? L L L22
63.若曲线积分
A. ?? L(x2?3y)dx?(ax?sin2y)dy与路径无关,则常数a?( )。
11 B. ?3 C. D. 3 33x2y2264.设L表示椭圆2?2?1,方向逆时针,则?(x?y)dx?( )
Lab A.?ab B. ??ab C. a?b D. 0 65.设L是从点A(1,0)到点B(-1,2)的有向弧段,则曲线积分
22?(x?y)ds?( )。
LA.2 B. 22 C. 2 D. 0 66.曲线弧A. C.
上的曲线积分和
上的曲线积分有关系 ( )
??ABf(x,y)ds???f(x,y)ds B. ?BABAABf(x,y)ds??f(x,y)ds
BABAABf(x,y)ds??f(?x,?y)ds?0 D. ?f(x,y)ds??f(?x,?y)ds
AB67.设I?( ) A. C.
????zdv,其中??{(x,y,z,)x2?y2?z2?1,z?0},经球坐标变换后,I?
?2??00d??2d??r3sin?cos?dr B. ?d??d??r2sin?dr
012??1000?2?0d??d??rsin?cos?dr D. ?d??2d??r3sin?cos?dr
3000002
?12??1
68. 设L是y=4x从(0,0)到(1,2)的一段,则
2 22? Lyds?( )
A.
? 0x1?4x2dx B.? 1 0 1x2?y?y1???dy C. ?x1?dx
04?2? D.
? 01?4y2dy
22?yx?P?Qy?x69.设I???cx2?y2dx?x2?y2dy,,因为?y??x?(x2?y2)2,所以( )
A. 对任意闭曲线C,I?0;
B. 在曲线C不围住原点时,I?0; ?PC. 因与?Q在原点不存在,故对任意的闭曲线C,I?0;
?x?yD. 在闭曲线C围住原点时I=0,不围住原点时 I?0。 70. 级数
??(?1)nn?11。 (p?0)的敛散情况是( )pn