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Paul's Online Notes
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Home / Calculus III / Multiple Integrals / Triple Integrals
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Section 15.5 : Triple Integrals

  1. Evaluate 3241014x2yz3dzdydx Solution
  2. Evaluate 10z2030ycos(z5)dxdydz Solution
  3. Evaluate where E is the region below 4x + y + 2z = 10 in the first octant. Solution
  4. Evaluate \displaystyle \iiint\limits_{E}{{3 - 4x\,dV}} where E is the region below z = 4 - xy and above the region in the xy-plane defined by 0 \le x \le 2, 0 \le y \le 1. Solution
  5. Evaluate \displaystyle \iiint\limits_{E}{{12y - 8x\,dV}} where E is the region behind y = 10 - 2z and in front of the region in the xz-plane bounded by z = 2x, z = 5 and x = 0. Solution
  6. Evaluate \displaystyle \iiint\limits_{E}{{yz\,dV}} where E is the region bounded by x = 2{y^2} + 2{z^2} - 5 and the plane x = 1. Solution
  7. Evaluate \displaystyle \iiint\limits_{E}{{15z\,dV}} where E is the region between 2x + y + z = 4 and 4x + 4y + 2z = 20 that is in front of the region in the yz-plane bounded by z = 2{y^2} and z = \sqrt {4y} . Solution
  8. Use a triple integral to determine the volume of the region below z = 4 - xy and above the region in the xy-plane defined by 0 \le x \le 2, 0 \le y \le 1. Solution
  9. Use a triple integral to determine the volume of the region that is below z = 8 - {x^2} - {y^2} above z = - \sqrt {4{x^2} + 4{y^2}} and inside {x^2} + {y^2} = 4. Solution