I am trying to solve the triple integral xyz dxdydz where E is the surface bounded by E = {(x,y,z) ∈ R^3 : 4<= x^2+y^2+z^2<=9, x<=0, z<=0}. I am unsure what E actually means and what equations you are integrating between.If someone could help me understand this then I should be able to compute the final answer.
2026-03-29 04:42:47.1774759367
Triple Integrals in spherical coordinates bound by E
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This is an integral over $xyz$ over the spherical shell bound by the spheres of radii 2 and 3, in the quadrant $x\le 0$, $z\le 0$. Because the integrand contains the factor $y$ and for any $x$ and $z$ both $y$ are included, these contributions cancel, and the integral is zero.