Question

Write an iterated integral for ModifyingBelow Integral from nothing to nothing Integral from nothing to nothing Integral from nothing to nothing With Upper D f (x comma y comma z )dV where D is a sphere of radius 9 centered at​ (0,0,0). Use the order dy dz dx .

Answer 1

With the given order of integration, the interval over D is

$\displaystyle \iiint_D f(x,y,z) \, dV = \int_{-3}^{3} \int_{-\sqrt{9-x^2}}^{\sqrt{9-x^2}} \int_{-\sqrt{9-x^2-z^2}}^{\sqrt{9-x^2-z^2}} f(x,y,z) \, dy \, dz \, dx$