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Calc 3 12.5

 

<== Calculus 3
Number Question Answer
See the work
1. Evaluate \displaystyle \iiint_B z e^{x+y} dV where B is the box determined by
0 &le x &le 2, 0 &le y &le 3, and 0 &le z &le 1.
The value is .
1151.21 The work
2. Evaluate the triple integral \displaystyle \iiint_{E} xy \, dV where E is the solid tetrahedon with vertices (0,0,0), (3,0,0), (0,2,0), (0,0,2).

0.6 The work
3. Evaluate the triple integral \displaystyle \iiint_{E} x^4 e^y \, dV where E is bounded by the parabolic cylinder z = 36 -y^2 and the planes z = 0, x = 6, and x = -6.

12548357.13 The work
4. Evaluate the triple integral \displaystyle \iiint_{E} x \, dV where E is the solid bounded by the paraboloid x=10 y^2+ 10 z^2
and x = 10.

104.72 The work
5. Evaluate the triple integral \displaystyle \iiint_{E} z \, dV where E is the solid bounded by the cylinder y^2+  z^2 = 1600 and the planes x = 0, y = 8x and z = 0 in the first octant.

40000 The work
6. Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = 3 x^2
and the planes z = 0, z = 7 and y = 3.

28 The work
7. Find the volume of the solid enclosed by the paraboloids z = 16 \left(
x^{2} + y^{2} 
ight) and z = 8 - 16 \left( x^{2} + y^{2}

ight).

&pi The work
8. Express the integral \displaystyle \iiint_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 - 8x and y = 32.

1. \displaystyle \int_a^b
\int_{g_1(x)}^{g_2(x)} \int_{h_1(x,y)}^{h_2(x,y)}f(x,y,z) dz dy dx
a = b =
g_1(x) = g_2(x) =
h_1(x,y) = h_2(x,y) =

2. \displaystyle \int_a^b
\int_{g_1(y)}^{g_2(y)} \int_{h_1(x,y)}^{h_2(x,y)}f(x,y,z) dz dx dy
a = b =
g_1(y) = g_2(y) =
h_1(x,y) = h_2(x,y) =

3. \displaystyle \int_a^b
\int_{g_1(z)}^{g_2(z)} \int_{h_1(y,z)}^{h_2(y,z)}f(x,y,z) dx dy dz
a = b =
g_1(z) = g_2(z) =
h_1(y,z) = h_2(y,z) =

4. \displaystyle \int_a^b
\int_{g_1(y)}^{g_2(y)} \int_{h_1(y,z)}^{h_2(y,z)}f(x,y,z) dx dz dy
a = b =
g_1(y) = g_2(y) =
h_1(y,z) = h_2(y,z) =

5. \displaystyle \int_a^b
\int_{g_1(x)}^{g_2(x)} \int_{h_1(x,z)}^{h_2(x,z)}f(x,y,z) dy dz dx
a = b =
g_1(x) = g_2(x) =
h_1(x,z) = h_2(x,z) =

6. \displaystyle \int_a^b
\int_{g_1(z)}^{g_2(z)} \int_{h_1(x,z)}^{h_2(x,z)}f(x,y,z) dy dx dz
a = b =
g_1(z) = g_2(z) =
h_1(x,z) = h_2(x,z) =

1.
a = 0
b = 4
8x
32
0
y-8x

2.
a = 0
b = 32
0
y/8
0
y-8x

3.
a = 0
b = 32
z
32
0
(y-z)/8

4.
a = 0
b = 32
0
y
0
(y-z)/8

5.
a = 0
b = 4
0
32-8x
8x+z
32

6.
a = 0
b = 32
0
4 - z/8
8x + z
32

The work
9. question Answer The work
10. question Answer The work
11. question Answer The work
12. question Answer The work
13. question Answer The work
14. question Answer The work
15. question Answer The work