10.4: Triple Integrals
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- Evaluate ∭B(2x+3y2+4z3) dV, where B=[0,1]×[0,2]×[0,3].
- Evaluate ∭B(zsinx+y2) dV, where B=[0,π]×[0,1]×[−1,2].
- Evaluate ∭E(2x+5y−7z) dV, where E is the region in the first octant bounded by y=1−x, z=1, and z=2
- 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.
- Evaluate ∭E(x+2yz) dV, where E is the region in the first octant where x+y+z≤5, y≤x, and x≤1.
- Evaluate ∭Ey dV, where E is the unit sphere centered at the origin.
- Evaluate ∭Ex2 dV, where E is the region bounded by x=1−y2, x=y2−1, z=1, and z=2.
- Evaluate ∭E2x dV, where E is the region in the first octant bounded by x+y+z=4, y=2x, and x=2.
- Use a triple integral to find the volume of the region in the first octant bounded by the paraboloid z=1−x2−y2 and the planes y=x and x=0