Integrais múltiplas

O problema do volume
Dada uma função [math]f[/math] de duas variáveis, contínuas e não negativas numa região R no plano xy, encontrar o volume do sólido compreendido entre a superfície z = f(x,y) e a região 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[/img]
Integral Dupla em Regiões Retangulares
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[/img]
Como resolver?
Interpretação Geométrica de Integral Dupla em regiões retangulares

Information: Integrais múltiplas