来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/04 19:03:30
高数三重积分问题,如图题四.
0≤r≤t
0≤φ≤π
0≤θ≤2π
F(t)=∫∫∫f(r²)r²sinφdrdφdθ
=∫(0,2π)dθ∫(0,π)sinφdφ∫(0,t)f(r²)r²dr
=2π∫(0,π)sinφdφ ∫(0,t)f(r²)r²dr
=2π (-cosφ)|(0,π) · ∫(0,t)f(r²)r²dr
=4π∫(0,t)f(r²)r²dr
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