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Lesson: Convergence and Divergence of Improper Integrals

Worksheet • 21 Questions

Q1:

Determine whether the integral ο„Έ 𝑒 πœƒ πœƒ ∞ 0 πœƒ c o s s i n d is convergent or divergent.

  • Aconvergent
  • Bdivergent

Q2:

Determine whether the integral ο„Έ ο€Ή 𝑦 βˆ’ 3 𝑦  𝑦 ∞ βˆ’ ∞ 3 2 d is convergent or divergent.

  • Aconvergent
  • Bdivergent

Q3:

Determine whether the integral ο„Έ 1 3 βˆ’ 4 π‘₯ π‘₯ 0 βˆ’ ∞ d is convergent or divergent.

  • Aconvergent
  • Bdivergent

Q4:

Determine whether the integral ο„Έ 1 √ 1 + π‘₯ π‘₯ ∞ 0 4 d is convergent or divergent.

  • Aconvergent
  • Bdivergent

Q5:

Determine whether the integral ο„Έ π‘₯ √ 1 + π‘₯ π‘₯ ∞ 0 2 3 d is convergent or divergent.

  • Aconvergent
  • Bdivergent

Q6:

Determine whether the integral ο„Έ 𝛼 𝛼 ∞ 0 2 s i n d is convergent or divergent.

  • Aconvergent
  • Bdivergent

Q7:

Determine whether the integral ο„Έ π‘₯ π‘₯ π‘₯ ∞ 1 l n d is convergent or divergent.

  • Aconvergent
  • Bdivergent

Q8:

The integral ο„Έ 2 π‘Ÿ 0 βˆ’ ∞ π‘Ÿ d is convergent. What does it converge to?

  • A 1 2 l n
  • B 2 2 l n
  • C βˆ’ 1 2 l n
  • D βˆ’ 2 l n
  • E 2 2 l n

Q9:

The integral ο„Έ 𝑣 𝑣 + 2 𝑣 βˆ’ 3 ∞ 2 2 d is convergent. What does it converge to?

  • A l n 5 4
  • B0
  • C βˆ’ 5 4 l n
  • D βˆ’ 4 5 l n
  • E 4 5 l n

Q10:

The integral ο„Έ 1 π‘₯ + π‘₯ π‘₯ ∞ 1 2 d is convergent. What does it converge to?

  • A l n 2
  • B βˆ’ 1 2 l n
  • C βˆ’ 2 l n
  • D 1 2 l n
  • E0

Q11:

The integral ο„Έ 𝑧 𝑧 + 4 𝑧 0 βˆ’ ∞ 4 d is convergent. What does it converge to?

  • A βˆ’ πœ‹ 8
  • B βˆ’ πœ‹ 1 6
  • C πœ‹ 8
  • D πœ‹ 2
  • E βˆ’ πœ‹ 2

Q12:

The integral ο„Έ 1 ( π‘₯ βˆ’ 2 ) π‘₯ ∞ 3 3 2 d is convergent. What does it converge to?

Q13:

The integral ο„Έ π‘₯ √ π‘₯ + π‘₯ √ π‘₯ ∞ 1 d is convergent. What does it converge to?

  • A πœ‹ 2
  • B0
  • C 3 πœ‹ 2
  • D 3 πœ‹ 4
  • E πœ‹ 4

Q14:

The integral ο„Έ 𝑒 𝑝 ∞ 2 βˆ’ 5 𝑝 d is convergent. What does it converge to?

  • A 𝑒 5 βˆ’ 1 0
  • B βˆ’ 𝑒 5 βˆ’ 5
  • C βˆ’ 𝑒 5 βˆ’ 1 0
  • D βˆ’ 5 𝑒 βˆ’ 5
  • E 5 𝑒 βˆ’ 1 0

Q15:

The integral ο„Έ π‘₯ 𝑒 π‘₯ ∞ βˆ’ ∞ βˆ’ π‘₯ 2 d is convergent. What does it converge to?

Q16:

The integral ο„Έ 𝑧 𝑒 𝑧 0 βˆ’ ∞ 2 𝑧 d is convergent. What does it converge to?

  • A βˆ’ 1 4
  • B2
  • C 1 4
  • D βˆ’ 2
  • E 3 4

Q17:

The integral ο„Έ 𝑒 π‘₯ π‘₯ ∞ 1 βˆ’ 2 1 π‘₯ d is convergent. What does it converge to?

  • A 1 βˆ’ 1 𝑒
  • B 1 + 1 𝑒
  • C 1 βˆ’ 𝑒
  • D 1 𝑒 βˆ’ 1
  • E 1 𝑒

Q18:

The integral ο„Έ 𝑦 𝑒 𝑦 ∞ 2 βˆ’ 3 𝑦 d is convergent. What does it converge to?

  • A 7 𝑒 9 βˆ’ 6
  • B 7 𝑒 9 βˆ’ 3
  • C βˆ’ 7 𝑒 9 βˆ’ 6
  • D βˆ’ 6 3 𝑒 βˆ’ 3
  • E 6 3 𝑒 βˆ’ 6

Q19:

The integral ο„Έ 𝑒 𝑦 ∞ 0 βˆ’ √ 𝑦 d is convergent. What does it converge to?

Q20:

The integral ο„Έ π‘₯ π‘₯ π‘₯ ∞ 1 2 l n d is convergent. What does it converge to?

Q21:

Consider the integral ο„Έ 1 ( 2 π‘₯ + 1 ) π‘₯ ∞   d .

Determine whether the integral is convergent or divergent.

  • ADivergent
  • BConvergent

Determine the value of integration.

  • A 1 3 6
  • B βˆ’ 1 3 6
  • C 1 4
  • D βˆ’ 2 9
  • E 5 1 8
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