计算三重积分∫〈0—1〉dx∫〈0—1-x〉dy∫〈0—y/2〉[cos(z)/(2z-1)^2]d
- 培训职业
- 2025-05-06 11:50:04
交换积分次序为先x再y最后为z的三次积分:
∫〈0—1〉dx∫〈0—1-x〉dy∫〈0—y/2〉[cos(z)/(2z-1)^2]dz
=∫〈0—1/2〉dz∫〈2z—1〉dy∫〈0—1-y〉[cos(z)/(2z-1)^2]dz
=∫〈0—1/2〉[cos(z)/(2z-1)^2]dz∫〈2z—1〉(1-y)dy
=∫〈0—1/2〉(1/2)cos(z)dz=(1/2)sin(1/2)
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