Worksheet: Double Integrals over Rectangular Regions

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In this worksheet, we will practice evaluating a double integral over a rectangular region by using iterated integrals.

Q1:

Evaluate the double integral 1𝑥𝑦dd.

Q2:

Evaluate the double integral 𝑥(𝑥𝑦+𝑥)𝑥𝑦sindd rounding to three decimals.

Q3:

Evaluate the double integral 𝑥𝑦𝑥𝑦dd.

Q4:

Evaluate the double integral (𝑥+2)𝑥𝑦dd.

Q5:

Evaluate the double integral 𝑥(𝑥+𝑦)𝑥𝑦dd.

  • A113
  • B10
  • C53
  • D8
  • E12

Q6:

Evaluate the double integral (1−𝑦)𝑥𝑥𝑦dd.

  • A0
  • B76
  • C72
  • D16
  • E73

Q7:

Evaluate the double integral 𝑥𝑦𝑦𝑥𝑥𝑦cosdd.

  • A−12
  • B0
  • C13
  • D12
  • E2

Q8:

Evaluate the double integral 𝑥(𝑦−𝜋)𝑥𝑦sincosdd.

Q9:

Find the volume under the surface 𝑧=4𝑥𝑦 over the rectangle 𝑅=[0,1]×[0,1].

Q10:

Find the volume under the surface 𝑧=𝑥+𝑦 over the rectangle 𝑅=[0,1]×[0,1].

  • A1
  • B2
  • C712
  • D13
  • E112

Q11:

Find the volume under the surface 𝑧=𝑥+𝑥𝑦+𝑦of the rectangular prism with base 𝑅=[1,2]×[0,2].

  • A975
  • B106
  • C80
  • D1475
  • E97

Q12:

Find the volume under the surface 𝑧=𝑒() over the rectangle 𝑅=[0,1]×[−1,1].

  • A−1−1𝑒+(𝑒−1)𝑒
  • B−1+1𝑒−(𝑒−1)𝑒
  • C−1+1𝑒+(𝑒−1)𝑒
  • D−1−1𝑒−(𝑒−1)𝑒
  • E𝑒

Q13:

Evaluate the double integral 𝑥𝑦𝑒𝑥𝑦∞∞dd.

  • A14
  • B12
  • C4
  • D−14
  • E2

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