Lesson Worksheet: Improper Integrals: Discontinuous Integrands Mathematics • Higher Education

In this worksheet, we will practice evaluating improper integrals where the integrand has a vertical asymptote.

Q1:

The integral ο„Έπ‘Ÿπ‘Ÿπ‘ŸοŠ§οŠ¦lnd is convergent. What does it converge to?

  • Aβˆ’14
  • Bβˆ’12
  • C14
  • D12
  • E0

Q2:

Determine whether the integral ο„Έ1π‘₯π‘₯d is convergent or divergent.

  • ADivergent
  • BConvergent

Q3:

Determine whether the integral ο„Έπ‘₯(π‘₯+1)π‘₯d is convergent or divergent.

  • Aconvergent
  • Bdivergent

Q4:

The integral ο„Έ1√1βˆ’π‘₯π‘₯d is convergent. What does it converge to?

  • Aβˆ’πœ‹2
  • Bπœ‹4
  • C0
  • Dβˆ’πœ‹4
  • Eπœ‹2

Q5:

The integral ο„Έ1√5βˆ’π‘₯π‘₯d is convergent. What does it converge to?

  • Aβˆ’345
  • B235
  • C345
  • Dβˆ’325
  • E325

Q6:

The integral ο„Έ1√π‘₯+2π‘₯οŠͺd is convergent. What does it converge to?

  • A6
  • Bβˆ’32
  • C323
  • Dβˆ’323
  • Eβˆ’2

Q7:

Determine whether the integral 𝑒π‘₯π‘₯οŠ§οŠ¦οŠ©οŽ ο‘d is convergent or divergent.

  • Aconvergent
  • Bdivergent

Q8:

The integral 𝑒π‘₯π‘₯οŠ¦οŠ±οŠ§οŠ©οŽ ο‘d is convergent. What does it converge to?

  • A2𝑒
  • Bβˆ’1𝑒
  • Cβˆ’2𝑒
  • Dβˆ’2𝑒
  • E𝑒

Q9:

Determine whether the integral ο„Έπœƒπœƒο‘½οŽ‘οŠ¦οŠ¨tand is convergent or divergent.

  • Adivergent
  • Bconvergent

Q10:

The integral ο„Έπœƒβˆšπœƒπœƒο‘½οŽ‘οŠ¦cossind is convergent. What does it converge to?

This lesson includes 9 additional questions and 9 additional question variations for subscribers.

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