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  • Pregunta: Express the integral ∭Ef(x,y,z)dV as an iterated integral in six different ways, where E is the solid bounded by z=0,x=0,z=y−x and y=2. 1. ∫0b∫g1(x)g1(x)∫h1(x,y)h2(x,y)f(x,y,z)dzdydx a=g1(x)=h1(x,y)=b=g2(x)=h2(x,y)= 2. ∫ab∫g1(y)g2(y)∫h1(x,y)h1(x,y)f(x,y,z)dzdxdy a=g1(y)=h1(x,y)=b=g2(y)=h2(x,y)= a=g1(z)=zb=g2(z)=h2(y,z)= 4.


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    Solución
    Paso 1

    Answer:- Given z=0,x=0,z=y−xandy=2


    (4). ∫ab∫g1(y)g2(y)∫h1(y,z)h2(y,z)f(x,y,z)dx.dz.dy

    Then

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Texto de la transcripción de la imagen:
Express the integral ∭E​f(x,y,z)dV as an iterated integral in six different ways, where E is the solid bounded by z=0,x=0,z=y−x and y=2. 1. ∫0b​∫g1​(x)g1​(x)​∫h1​(x,y)h2​(x,y)​f(x,y,z)dzdydx a=g1​(x)=h1​(x,y)=​b=g2​(x)=h2​(x,y)=​ 2. ∫ab​∫g1​(y)g2​(y)​∫h1​(x,y)h1​(x,y)​f(x,y,z)dzdxdy a=g1​(y)=h1​(x,y)=​b=g2​(y)=h2​(x,y)=​ a=g1​(z)=z​b=g2​(z)=h2​(y,z)=​  4. ∫ab​∫g1​(y)g2​(y)​∫h1​(y,z)h2​(y,z)​f(x,y,z)dxdzdya=b=g1​(y)=g2​(y)=h1​(y,z)=h2​(y,z)= 5. ∫ab​∫g1​(x)g2​(x)​∫h1​(x,z)h2​(x,z)​f(x,y†,z)dydzdxa=b=g1​(x)=g2​(x)=h1​(x,z)=h2​(x,z)= 6. ∫ab​∫g1​(z)g2​(z)​∫h1​(x,z)h2​(x,z)​f(x,y,z)dydxdza=g1​(z)=g2​(z)=h1​(x,z)=h2​(x,z)=​