sbcardinals sbcardinals

12-08-2022
Mathematics

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Set up a triple integral for the volume of the solid enclosed by the planes x = 0, y = 0, z = 0 and x + y + z = 2.

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LammettHash LammettHash

12-08-2022

[tex]\displaystyle \int_0^2 \int_0^{2-x} \int_0^{2-x-y} dz \, dy \, dx = \int_0^2 \int_0^{2-x} (2-x-y) \, dy \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^2 (x-2)^2 \, dx = \boxed{\frac43}[/tex]

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