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=5y and x2=16−y 1∫ab∫g1(x)g2(x)∫h1(x,y)h1(x,y)f(x,y,z)dzdydxa=−Ab=g1(x)=g2(x)=h1(x,y)=0h2(x,y)=5y 2. ∫ab∫g1(y)g=(y)∫h1(x,y)gn(x,y)f(x,y,z)dzdxdya=0=16g2(y)=g1(y)=h1(x,y)=h2(x,y)=5y 3. ∫ab∫0,(0)n0(v)∫h2(y,z)h2(y,e)f(x,y,z)dxdydz a=−4]ab=4

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Resuelto Express the integral ∭Ef(x,y,z)dV as an iterated

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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=5y and x2=16−y 1∫ab∫g1(x)g2(x)∫h1(x,y)h1(x,y)f(x,y,z)dzdydxa=−Ab=g1(x)=g2(x)=h1(x,y)=0h2(x,y)=5y 2. ∫ab∫g1(y)g=(y)∫h1(x,y)gn(x,y)f(x,y,z)dzdxdya=0=16g2(y)=g1(y)=h1(x,y)=h2(x,y)=5y 3. ∫ab∫0,(0)n0(v)∫h2(y,z)h2(y,e)f(x,y,z)dxdydz a=−4]ab=4

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Texto de la transcripción de la imagen:

Express the integral

∭_{E} f (x, y, z) d V

as an iterated integral in six different ways, where

E

is the solid bounded by

z = 0, z = 5 y

and

x^{2} = 16 - y

1 \int_{a}^{b} \int_{g_{1} (x)}^{g 2 (x)} \int_{h_{1} (x, y)}^{h_{1} (x, y)} f (x, y, z) d z d y d x a = - A b = g_{1} (x) = g_{2} (x) = h_{1} (x, y) = 0 h_{2} (x, y) = 5_{y} 2. \int_{a}^{b} \int_{g_{1} (y)}^{g = (y)} \int_{h_{1} (x, y)}^{g_{n} (x, y)} f (x, y, z) d z d x d y a = 0 = 16 g_{2} (y) = g_{1} (y) = h_{1} (x, y) = h_{2} (x, y) = 5 y

\int_{a}^{b} \int_{0, (0)}^{n_{0} (v)} \int_{h_{2} (y, z)}^{h_{2} (y, e)} f (x, y, z) d x d y d z

a = - 4]_{a} b = 4

g_{1} (z) = g_{2} (z) = h_{3} (y, z) = h_{2} (y, z) = \frac{z}{4}

4. \int_{a}^{b} \int_{n_{0} (x)}^{n_{0} (y)} \int_{h_{1} (x, a)}^{h_{0} (y, -)} f (x, y, z) d x d z d y a = b = 64 g_{i} (v) = g_{2} (y) = h_{1} (y, z) = h_{2} (y, z) =

a = 0 b g_{1} (x) = 0] g (x) h_{1} (x, z) = h_{2} (x, z) =

\int_{a}^{b} \int_{g_{1} (z)}^{g_{2} (z)} \int_{h_{1} (y, z)}^{h_{2} (y, z)} f (x, y, z) d x d y d z

a = b =

g_{1} (z) = g_{2} (z) = 64 - 5 x^{2}

h_{1} (y, z) = h_{2} (y, z) = \frac{z}{4}

\int_{a}^{b} \int_{g_{1} (y)}^{g_{2} (y)} \int_{h_{1} (y, z)}^{h_{2} (y, z)} f (x, y, z) d x d z d y

a = b =

g_{1} (y) = g_{2} (y) = \frac{z}{4}

h_{1} (y, z) =

\int_{a}^{b} \int_{g_{1} (x)}^{g_{2} (x)} \int_{h_{1} (x, z)}^{h_{2} (x, z)} f (x, y, z) d y d z d x

a = b =

g_{1} (x) = 0 g_{2} (x) =

h_{1} (x, z) = h_{2} (x, z) =

\int_{a}^{b} \int_{g_{1} (z)}^{g_{2} (z)} \int_{\underline{h_{1} (z, x)}}^{h_{2} (z, z)} f (x, y, z) d y d x d z

a = b =

g_{1} (z) = g_{2} (z) = \frac{z}{4}

h_{1} (x, z) =

h_{2} (x, z) =