Worksheet: Double Integrals over Rectangular Regions

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.

  • A 1 1 3
  • B10
  • C 5 3
  • D8
  • E12

Q6:

Evaluate the double integral (1𝑦)𝑥𝑥𝑦dd.

  • A0
  • B 7 6
  • C 7 2
  • D 1 6
  • E 7 3

Q7:

Evaluate the double integral 𝑥𝑦𝑦𝑥𝑥𝑦cosdd.

  • A 1 2
  • B0
  • C 1 3
  • D 1 2
  • E2

Q8:

Evaluate the double integral 𝑥(𝑦𝜋)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
  • C 7 1 2
  • D 1 3
  • E 1 1 2

Q11:

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

  • A 9 7 5
  • B106
  • C80
  • D 1 4 7 5
  • E97

Q12:

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

  • A 1 1 𝑒 + ( 𝑒 1 ) 𝑒
  • B 1 + 1 𝑒 ( 𝑒 1 ) 𝑒
  • C 1 + 1 𝑒 + ( 𝑒 1 ) 𝑒
  • D 1 1 𝑒 ( 𝑒 1 ) 𝑒
  • E 𝑒

Q13:

Evaluate the double integral 𝑥𝑦𝑒𝑥𝑦dd.

  • A 1 4
  • B 1 2
  • C4
  • D 1 4
  • E2

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.