Worksheet: Triple Integrals

In this worksheet, we will practice evaluating triple integrals.

Q1:

Evaluate the triple integral 𝑥𝑦𝑧𝑥𝑦𝑧ddd.

Q2:

Evaluate the triple integral 1𝑥𝑦𝑧ddd.

Q3:

Evaluate the triple integral 𝑥𝑦𝑧𝑧𝑦𝑥ddd.

  • A 1 4 8
  • B 1 2 4
  • C 1 3 0
  • D 1 1 2
  • E 1 6

Q4:

Evaluate the triple integral 𝑧𝑥𝑥𝑧𝑦ddd.

  • A 1 3
  • B1
  • C 1 2
  • D 1 6
  • E 5 6

Q5:

Evaluate the triple integral 𝑦𝑧𝑥𝑧𝑦ddd.

  • A 1 2 8 5
  • B 3 4 1 9
  • C 5 1 2 2 0
  • D1,023
  • E 1 , 0 2 3 4 0

Q6:

Evaluate the triple integral 1𝑧𝑦𝑥ddd.

  • A 1 6
  • B 1 3
  • C 1 2
  • D 1 4
  • E 1 2

Q7:

Evaluate the triple integral 𝑧𝑒𝑥𝑦𝑧ddd.

  • A ( 𝑒 4 )
  • B 1 4 ( 𝑒 2 )
  • C 1 2 ( 𝑒 2 )
  • D 𝑒 4
  • E ( 𝑒 2 )

Q8:

Evaluate the triple integral 𝑧𝑥𝑥𝑦𝑧ddd.

  • A 1 2
  • B 1 3
  • C1
  • D 1 7 2
  • E 1 1 2

Q9:

Find the volume 𝑉 of the solid bounded by the three coordinate planes and the plane 3𝑥+2𝑦+5𝑧=6.

Q10:

Find the volume of the solid 𝑆 bounded by the three coordinate planes, the plane 𝑥+𝑦+𝑧=2 from above, and the plane 𝑧=𝑥+𝑦 from below.

  • A 4 3
  • B 1 3
  • C 2 3
  • D 4 3
  • E2

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