- #1
Another
- 104
- 5
Homework Statement
Find the volume in octane 1 enclosed.
x + y + 2z = 2
2x + 2y +z = 4
∫∫∫ dV
Homework Equations
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The Attempt at a Solution
∫∫∫ dv = [∫(0⇒2) [∫(2-2z)⇒(2-½z) [∫(2-2z-y)⇒(2-½z-y) dx] dy] dz]
= [∫(0⇒2) [∫(2-2z)⇒(2-½z) [x]|(2-2z-y)⇒(2-½z-y) dy] dz]
= [∫(0⇒2) [∫(2-2z)⇒(2-½z) (2-½z-y)-(2-2z-y) dy] dz]
= [∫(0⇒2) [∫(2-2z)⇒(2-½z) (3/4)z dy] dz]
= [∫(0⇒2) [¾yz]|(2-2z)⇒(2-½z) dz]
= [∫(0⇒2) ¾z[(2-½z)-(2-2z)] dz]
= [∫(0⇒2) ¾z^2 dz]
= (¾)(⅓) z^3 |(0⇒2)
= (3/12) [2^3 - 0^3]
= (3/12) (8)
= 2
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Am I wrong?
I do not understand some time i got the answer above 2 when i changed dxdydz dydzdx and dzdydx
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