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Triple integrals practice problems

Integrate over a box, one variable at a time. 30 problems with worked solutions; in 30 of them every equation is proved by a computer algebra system.

Evaluate \( \displaystyle \iiint_B x^{2} z \, dV \) where \( \displaystyle B = [0, 2] \times [0, 1] \times [0, 2] \).
Problem 11.43easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x^{2} z \, dV \) where \( \displaystyle B = [0, 3] \times [0, 1] \times [0, 3] \).
Problem 11.44easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B 2 x z \, dV \) where \( \displaystyle B = [0, 1] \times [0, 3] \times [0, 1] \).
Problem 11.45easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B 2 x z \, dV \) where \( \displaystyle B = [0, 1] \times [0, 3] \times [0, 3] \).
Problem 11.46easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x^{2} z \, dV \) where \( \displaystyle B = [0, 3] \times [0, 1] \times [0, 2] \).
Problem 11.47easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x + y + z \, dV \) where \( \displaystyle B = [0, 1] \times [0, 3] \times [0, 2] \).
Problem 11.48easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x^{2} z \, dV \) where \( \displaystyle B = [0, 3] \times [0, 2] \times [0, 3] \).
Problem 11.49easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x y z \, dV \) where \( \displaystyle B = [0, 2] \times [0, 1] \times [0, 2] \).
Problem 11.50easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B 2 x z \, dV \) where \( \displaystyle B = [0, 2] \times [0, 1] \times [0, 3] \).
Problem 11.51easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x + y + z \, dV \) where \( \displaystyle B = [0, 1] \times [0, 2] \times [0, 1] \).
Problem 11.52easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x + y + z \, dV \) where \( \displaystyle B = [0, 1] \times [0, 3] \times [0, 1] \).
Problem 11.53easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x + y + z \, dV \) where \( \displaystyle B = [0, 1] \times [0, 2] \times [0, 2] \).
Problem 11.54easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x^{2} z \, dV \) where \( \displaystyle B = [0, 3] \times [0, 3] \times [0, 3] \).
Problem 11.55easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x^{2} z \, dV \) where \( \displaystyle B = [0, 3] \times [0, 2] \times [0, 2] \).
Problem 11.56easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x y z \, dV \) where \( \displaystyle B = [0, 2] \times [0, 3] \times [0, 3] \).
Problem 11.57easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x^{2} z \, dV \) where \( \displaystyle B = [0, 2] \times [0, 2] \times [0, 2] \).
Problem 11.88easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x^{2} z \, dV \) where \( \displaystyle B = [0, 2] \times [0, 1] \times [0, 3] \).
Problem 11.89easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x y + z \, dV \) where \( \displaystyle B = [0, 1] \times [0, 3] \times [0, 1] \).
Problem 11.90easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x y z \, dV \) where \( \displaystyle B = [0, 2] \times [0, 3] \times [0, 1] \).
Problem 11.91easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x y + z \, dV \) where \( \displaystyle B = [0, 1] \times [0, 2] \times [0, 3] \).
Problem 11.92easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x + y + z \, dV \) where \( \displaystyle B = [0, 3] \times [0, 2] \times [0, 1] \).
Problem 11.93easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x^{2} z \, dV \) where \( \displaystyle B = [0, 1] \times [0, 1] \times [0, 2] \).
Problem 11.94easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B 2 x z \, dV \) where \( \displaystyle B = [0, 3] \times [0, 1] \times [0, 1] \).
Problem 11.95easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x^{2} z \, dV \) where \( \displaystyle B = [0, 1] \times [0, 3] \times [0, 1] \).
Problem 11.96easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x^{2} z \, dV \) where \( \displaystyle B = [0, 1] \times [0, 1] \times [0, 1] \).
Problem 11.97easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x y z \, dV \) where \( \displaystyle B = [0, 2] \times [0, 1] \times [0, 1] \).
Problem 11.98easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B 2 x z \, dV \) where \( \displaystyle B = [0, 1] \times [0, 2] \times [0, 1] \).
Problem 11.99easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x y + z \, dV \) where \( \displaystyle B = [0, 3] \times [0, 1] \times [0, 2] \).
Problem 11.100easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x + y + z \, dV \) where \( \displaystyle B = [0, 1] \times [0, 1] \times [0, 3] \).
Problem 11.101easy✓ Every equation proved
Evaluate \( \displaystyle \iiint_B x y + z \, dV \) where \( \displaystyle B = [0, 1] \times [0, 2] \times [0, 2] \).
Problem 11.102easy✓ Every equation proved