Worksheet: Triple Integrals

In this worksheet, we will practice evaluating triple integrals.

Q1:

Evaluate the triple integral ο„Έο„Έο„Έπ‘₯𝑦𝑧π‘₯π‘¦π‘§οŠ©οŠ¦οŠ¨οŠ¦οŠ§οŠ¦ddd.

Q2:

Evaluate the triple integral ο„Έο„Έο„Έ1π‘₯π‘¦π‘§οŠ¨οŠ§οŠͺddd.

Q3:

Evaluate the triple integral ο„Έο„Έο„Έπ‘₯𝑦𝑧𝑧𝑦π‘₯οŠ§οŠ¦ο—οŠ¦ο˜οŠ¦ddd.

  • A148
  • B124
  • C130
  • D112
  • E16

Q4:

Evaluate the triple integral 𝑧π‘₯π‘₯π‘§π‘¦οŒΎοŠ§ο˜οŠ¦οŠ¦οŠ¨οŽ ο‘‘ddd.

  • A13
  • B1
  • C12
  • D16
  • Eβˆ’56

Q5:

Evaluate the triple integral 𝑦𝑧π‘₯π‘§π‘¦οŠ¨οŠ§ο˜οŠ¦ο™οŠ¦οŽ‘οŽ‘ddd.

  • A1285
  • B3419
  • C51220
  • D1,023
  • E1,02340

Q6:

Evaluate the triple integral ο„Έο„Έο„Έ1𝑧𝑦π‘₯οŠ§οŠ¦οŠ§οŠ±ο—οŠ¦οŠ§οŠ±ο—οŠ±ο˜οŠ¦ddd.

  • A16
  • B13
  • Cβˆ’12
  • D14
  • E12

Q7:

Evaluate the triple integral 𝑧𝑒π‘₯π‘¦π‘§οŠ§οŠ¦ο™οŠ¦ο˜οŠ¦ο˜οŽ‘ddd.

  • A(π‘’βˆ’4)
  • B14(π‘’βˆ’2)
  • C12(π‘’βˆ’2)
  • D𝑒4
  • E(π‘’βˆ’2)

Q8:

Evaluate the triple integral 𝑧π‘₯π‘₯π‘¦π‘§οŠ§οŠ¦ο™οŠ¦ο˜οŠ¦οŠ¨ddd.

  • A12
  • B13
  • C1
  • D172
  • E112

Q9:

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

Q10:

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

  • Aβˆ’43
  • B13
  • C23
  • D43
  • E2

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