计算三重积分（其中Ω:x²+y²+z²)≤1,

计算三重积分<img src='https://img2.soutiyun.com/ask/2020-10-30/97291958752518.png' />其中Ω由圆锥面<img src='https://img2.soutiyun.com/ask/2020-10-30/972919603836112.png' />和球面x²+y²+(z-1)²=1所围成.

计算<img src='https://img2.soutiyun.com/ask/2020-12-28/97804069890239.png' />dxdy,其中f(u)具有连续的导数,(s)为锥面<img src='https://img2.soutiyun.com/ask/2020-12-28/978040711796127.png' />与两球面x²+y²十z²=1,x²+y²+z²=4所围立体的表面外侧.

<img src='https://img2.soutiyun.com/ask/2021-01-10/979142709737969.png' />,D是由抛物线y=x²与0x轴和直线x=1围成的区域.(计算二重积分)

计算曲线积分<img src='https://img2.soutiyun.com/ask/2021-01-11/979212178154824.jpg' />其中 (1)l为自点(a,0)经过上半圆周y=<img src='https://img2.soutiyun.com/ask/2021-01-11/979212192236629.jpg' />(a＞0)到点(-a,0); (2)l为自点(a,0)沿圆周x²+y²=a²的直径到点(-a,0); (3)l为逆时针方向的圆周x²+y²=a². <img src='https://img2.soutiyun.com/ask/2021-01-11/979212223884439.jpg' />

A．πa⁴ B． -πa⁴ C． -（π／2）a⁴ D． （π／2）a⁴

用直线<img src='https://img2.soutiyun.com/ask/2020-11-14/974186997169411.png' />把域1≤x≤2,1≤y≤3分为许多矩形.作出函数f(x,y)=x³+y²在此区域的积分下和S与积分上和<img src='https://img2.soutiyun.com/ask/2020-11-14/974187031813393.png' />当n→∞时,上和与下和的极限等于多少？

化三重积分<img src='https://img2.soutiyun.com/ask/2020-12-22/977522841488233.png' />为三次积分，其中积分区域Ω分别是: (1)由双曲抛物面xy=z及平面x+y-1=0,z=0所围成的闭区域; (2)由曲面z=x²+y²及平面Z=1所围成的闭区域

对积分<img src='https://img2.soutiyun.com/ask/2021-01-06/978807191352268.png' />进行极坐标变换并写出变换后不同顺序的累次积分: (1)当D为由不等式a²≤x²+y²≤b²,y≥0所确定的区域. (2)D={(x,y)|x²+y²≤y,x≥0l}; (3)D={(x,y)|0≤x≤1,0＜x+y≤1}

沿圆周l(x²+y²=9)正方向的曲线积分<img src='https://img2.soutiyun.com/ask/2021-01-11/979220343348846.jpg' />=().

计算<img src='https://img2.soutiyun.com/ask/2020-11-02/973163357083237.png' />其中L为曲线x²+y²=-2y.

利用三重积分计算下列由曲面所围立体的质心(设密度ρ=1): (1)z²=x²+y²,z=1; (2)<img src='https://img2.soutiyun.com/ask/2020-11-25/975183822416377.png' />,<img src='https://img2.soutiyun.com/ask/2020-11-25/975183835201108.png' />(A＞a＞0),z=0; (3)z=x²+y²,x+y=a,x=0,y=0,z=0.

计算<img src='https://img2.soutiyun.com/ask/2020-12-08/976286599693925.jpg' />，[1+x²+y²]表示不超过[1+x²+y²]的最大整数，其中D={(x，y)|x²+y²≤√2，x≥0，y≥0}。

设习是球Ω的表面x²+y²+z²=a²的外侧,<img src='https://img2.soutiyun.com/ask/2020-11-02/973176956181061.png' />计算曲面积分<img src='https://img2.soutiyun.com/ask/2020-11-02/973176967115687.png' />的过程如下: <img src='https://img2.soutiyun.com/ask/2020-11-02/973176983472622.png' /> 问上述计算是否正确？为什么？若错了,则改正之.

A．I≤-36π B． -36π≤I＜36π C． 36π≤I≤100π D． I＞100π

计算<img src='https://img2.soutiyun.com/ask/2020-12-09/976355118693535.jpg' />，其中L为第一象限中由x轴，y=x及x²+y²=4围成的曲线段。

<img src='https://img2.soutiyun.com/ask/2021-01-11/979216841161532.jpg' />,S为圆柱体[x²+y≤a²,0≤z≤h]的表面.(计算曲面积分)

设Ω=|(x,y,z)|x²+y²+z²≤1|则<img src='https://img2.soutiyun.com/ask/2021-01-10/979150367436964.png' />=().

计算<img src='https://img2.soutiyun.com/ask/2021-01-02/978464841600073.png' />其中D是由直线y=0;y=1及双曲线x²-y²=1所围成的闭区域

设f(u)可微，且f(0)=0。求<img src='https://img2.soutiyun.com/ask/2020-12-08/976287573353616.jpg' />，其中Ω：x²+y²+z²≤t²。

计算<img src='https://img2.soutiyun.com/ask/2020-12-08/976285825293632.jpg' />，其中D：x²+y²≤1。