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Lesson: Double Integrals over General Regions

Worksheet • 10 Questions

Q1:

Evaluate the double integral ο„Έ ο„Έ π‘₯ π‘₯ 𝑦 πœ‹ 0 𝑦 0 s i n d d .

  • A πœ‹
  • B0
  • C 1 βˆ’ πœ‹
  • D 1 βˆ’ πœ‹ 2
  • E πœ‹ 2

Q2:

Evaluate the double integral ο„Έ ο„Έ 1 π‘₯ 𝑦 2 0 𝑦 0 d d .

Q3:

Evaluate the double integral ο„Έ ο„Έ 2 𝑦 π‘₯ 1 0 π‘₯ 0 2 d d .

  • A 2 3
  • B1
  • C 2 π‘₯ 2
  • D 2 π‘₯
  • E2

Q4:

Evaluate the double integral ο„Έ ο„Έ π‘₯ 𝑦 π‘₯ 𝑦 πœ‹ 2 0 𝑦 0 c o s s i n d d .

  • A πœ‹ 4
  • B 1 3
  • C πœ‹ 2
  • D 2 πœ‹ 3
  • E πœ‹

Q5:

Evaluate the double integral ο„Έ ο„Έ 𝑒 π‘₯ 𝑦 2 0 2 𝑦 0 𝑦 2 d d .

  • A 𝑒 βˆ’ 1 4
  • B 𝑒 βˆ’ 1 2
  • C 2 𝑒 βˆ’ 1 4
  • D 𝑒 4
  • E 1 βˆ’ 𝑒 4

Q6:

Evaluate the double integral ο„Έ ο„Έ 2 4 𝑦 π‘₯ 𝑦 π‘₯ 1 0 1 √ π‘₯ 2 d d .

Q7:

Evaluate the double integral ο„Έ ο„Έ 4 π‘₯ 𝑦 π‘₯ . 2 1 π‘₯ 0 l n d d

  • A 8 2 βˆ’ 3 l n
  • B l n 4 βˆ’ 3 4
  • C 8 2 βˆ’ 4 l n
  • D 4 2 βˆ’ 4 l n
  • E 4 2 βˆ’ 3 l n

Q8:

Find the volume 𝑉 of the solid bounded by the three coordinate planes and the plane π‘₯ + 𝑦 + 𝑧 = 1 .

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

Q9:

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.

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

Q10:

Evaluate ο„Έ ο„Έ ο€Ό π‘₯ + 𝑦 2  ο€» π‘₯ βˆ’ 𝑦 2  𝐴 𝑅 s i n c o s d , where 𝑅 is the triangle with the vertices ( 0 , 0 ) , ( 2 , 0 ) , and ( 1 , 1 ) .

  • A 1 βˆ’ 2 2 s i n
  • B 1 + 2 s i n
  • C s i n 2 2
  • D 1 + 2 2 s i n
  • E 1 βˆ’ 2 s i n
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