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mathstina
Evaluate the integral ∭(xz+3z)dV,where E is the region bounded by the cylinder x^2 +z^2 = 9 and the planes x+y=3,z=0 and y=0 above the xy-plane.
Im just donig these myself so I dont know how much help I can be, but the tricky part is setting up the limits in the correct order. I think the first limit is x + y = 3 so it would be -3 to 3 for the first one (I think)
could you start by drawing picture?
thats e part i confused abt. the region ...
|dw:1353429220967:dw| draw your cylinder first
draw your planes |dw:1353429469502:dw|
|dw:1353429578503:dw| this is your last plane ... show how is the region gonna look like?
ok. hw to find the limits?
lol ... first of all picture your region ... then you will find the limits.
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ok. then... i m nt strong in this chpt.
first you need to visualize ... then approach the problem. |dw:1353430430927:dw|
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ok so far i unerstand. thanks . i need ur continual assistance; steps to e solution. i need to sign out. cya.
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if possible only could write the steps of the integration and the final ans.
do you have final answer?
from wolf i got around 64.8 http://www.wolframalpha.com/input/?i=Integration [Integration[Integration[xz%2B3z%2C+{y%2C+0%2C+3-x}]%2C+{z%2C+0%2C+sqrt%289+-+x^2%29}]%2C+{x%2C+0%2C+3}]