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Mathematics LibreTexts

10.4: Triple Integrals

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  1. Evaluate B(2x+3y2+4z3) dV, where B=[0,1]×[0,2]×[0,3].
     
  2. Evaluate B(zsinx+y2) dV, where B=[0,π]×[0,1]×[1,2].
     
  3. Evaluate E(2x+5y7z) dV, where E is the region in the first octant bounded by y=1x, z=1, and z=2
     
  4. Evaluate E(ylnx+z) dV, where E is the region in the first octant bounded by y=lnx, x=1, x=e, and z=1.
     
  5. Evaluate E(x+2yz) dV, where E is the region in the first octant where x+y+z5, yx, and x1.
     
  6. Evaluate Ey dV, where E is the unit sphere centered at the origin.
     
  7. Evaluate Ex2 dV, where E is the region bounded by x=1y2, x=y21, z=1, and z=2.
     
  8. Evaluate E2x dV, where E is the region in the first octant bounded by x+y+z=4, y=2x, and x=2.
     
  9. Use a triple integral to find the volume of the region in the first octant bounded by the paraboloid z=1x2y2 and the planes y=x and x=0

10.4: Triple Integrals is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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