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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,z=6y and x2=36−y. 1. ∫ab∫g1(x)g2(x)∫h1(x,y)h2(x,y)f(x,y,z)dzdydxa=□b=6g1(x)=x2g2(x)=h1(x,y)=0h2(x,y)= 2. ∫ab∫g1(y)g2(y)∫h1(x,y)h2(x,y)f(x,y,z)dzdxdya=□b=g1(y)=−sqrt(36−y)g2(y)=h1(x,y)=0h2(x,y)=6y 4.

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    To express the integral ∭ f(x, y, z) dV as an iterated integral in six different ways, we need to co...

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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,z=6y and x2=36−y.  1. ∫ab​∫g1​(x)g2​(x)​∫h1​(x,y)h2​(x,y)​f(x,y,z)dzdydxa=□b=6g1​(x)=x2g2​(x)=h1​(x,y)=0h2​(x,y)=​  2. ∫ab​∫g1​(y)g2​(y)​∫h1​(x,y)h2​(x,y)​f(x,y,z)dzdxdya=□b=g1​(y)=−sqrt(36−y)g2​(y)=h1​(x,y)=0h2​(x,y)=6y​  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)=−gg2​​(x)=h1​(x,z)=h2​(x,z)=​  6. ∫ab​∫g1​(z)g2​(z)​∫h1​(x,z)h2​(x,z)​f(x,y,z)dydxdza=□′b=g1​(z)=g2​(z)=h1​(x,z)=−h2​(x,z)=​