a) Find the volume of the solid E 4x² + 4y², bounded by z = V z = x? + y + z², x 2 0, y 2 0, and z < 0. Justify your choice of the coordinates system for the integration.

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Solve (a) Part only in 30 min and take a thumb up plz solve now
1:05
O 4G ll ul i 82%
Find the volume of the solid E
bounded by z = V4x2 + 4y²,
z = x? + y? + z², x > 0, y 2 0, and
z < 0. Justify your choice of the coordinates
system for the integration.
b) |
bounded by y > 0, z > 0, x > 4z, and
16 > x? + y?. Evaluate the following triple
integral:
Let E be the solid that is
-4z dV.
E
Let E be the solid that is
c)
within the first octant, enclosed by
x + 2y + 4z = 4. Evaluate following triple
integral:
I.
dV.
E
Is it possible to change the order of
integrations in the above triple integral?
Justify your answer, and if it is possible, then
write down all the other possible settings of
the triple integral.
Transcribed Image Text:1:05 O 4G ll ul i 82% Find the volume of the solid E bounded by z = V4x2 + 4y², z = x? + y? + z², x > 0, y 2 0, and z < 0. Justify your choice of the coordinates system for the integration. b) | bounded by y > 0, z > 0, x > 4z, and 16 > x? + y?. Evaluate the following triple integral: Let E be the solid that is -4z dV. E Let E be the solid that is c) within the first octant, enclosed by x + 2y + 4z = 4. Evaluate following triple integral: I. dV. E Is it possible to change the order of integrations in the above triple integral? Justify your answer, and if it is possible, then write down all the other possible settings of the triple integral.
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