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Worksheet: Improper Integrals

Q1:

Is ο„Έ π‘₯ π‘₯ πœ‹ 0 t a n d an improper integral?

  • AYes
  • BNo

Q2:

Is ο„Έ π‘₯ π‘₯ πœ‹ 4 0 t a n d an improper integral?

  • Ayes
  • Bno

Q3:

Is ο„Έ 𝑒 π‘₯ ∞ 0 βˆ’ π‘₯ 3 d an improper integral?

  • Ayes
  • Bno

Q4:

Consider the integral ο„Έ 1 π‘₯ ( π‘₯ ) π‘₯ ∞ 𝑒 𝑝 l n d .

Find all possible values of 𝑝 for which the integral is convergent.

  • A 𝑝 < 1
  • B 𝑝 ≀ 1
  • C 𝑝 β‰₯ 1
  • D 𝑝 > 1
  • E 𝑝 = 1

Evaluate the integral for those values of 𝑝 .

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

Q5:

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