Hi i have the oppertunity to correct certain questions on a test, and I just wan

Question

Hi i have the oppertunity to correct certain questions on a test, and I just wanted to make sure I redid this correctly. I am mostly confused on the bounds of integration and the best way to determine them. Hopfuly my work makes sense. Something still seems wrong about the bounds. Is it 0 to 3z for the y bounds??

Let B be the tetrahedron with the vertices p1(0, 0, 0), p1(2, 0, 0), p3(1, 0, 1), p4(1,3, 1). Describe the region in set notation and set up the integral f(x, y, z)dV as an iterated integral with appropriate bounds. Calculate the moment of inertia of E with respect to the x-axis, assuming a constant density of 1. E = {(x, y, z)|0 le z le 1, z le x le 2 - z, 0 le y le 3z} f(x, y, z)dy dx dz Ix = (y2 + z2)p(x, y, z)dv p(x, y, z) = 1 Ix = (y2 + z2)f(x, y, z)dy dx dz

Explanation / Answer

you are correct

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