Worksheet: Improper Integrals: Discontinuous Integrands
In this worksheet, we will practice evaluating improper integrals where the integrand has a vertical asymptote.
Q1:
The integral is convergent. What does it converge to?
- A
- B0
- C
- D
- E
Q2:
Determine whether the integral is convergent or divergent.
- AConvergent
- BDivergent
Q3:
Determine whether the integral is convergent or divergent.
- Aconvergent
- Bdivergent
Q4:
The integral is convergent. What does it converge to?
- A0
- B
- C
- D
- E
Q5:
The integral is convergent. What does it converge to?
- A
- B
- C
- D
- E
Q6:
The integral is convergent. What does it converge to?
- A6
- B
- C
- D
- E
Q7:
Determine whether the integral is convergent or divergent.
- Adivergent
- Bconvergent
Q8:
The integral is convergent. What does it converge to?
- A
- B
- C
- D
- E
Q9:
Determine whether the integral is convergent or divergent.
- Aconvergent
- Bdivergent
Q10:
The integral is convergent. What does it converge to?
Q12:
Determine whether the integral is convergent or divergent.
- Adivergent
- Bconvergent
Q13:
Determine whether the integral is convergent or divergent.
- Aconvergent
- Bdivergent
Q14:
The integral is convergent. What does it converge to?
- A
- B
- C2
- D
- E
Q15:
Consider the integral .
Find all possible values of for which the integral is convergent.
- A
- B
- C
- D
- E
Evaluate the integral for those values of .
- A
- B
- C
- D
- E
Q16:
Consider the integral .
Find all possible values of for which the integral is convergent.
- A
- B
- C
- D
- E
Evaluate the integral for those values of .
- A
- B
- C
- D
- E
Q17:
Consider the integral . Which of the following is a correct characterization of this integral?
- AThe integral is undefined only if or is an integer multiple of .
- BThe integral is defined for all finite values of and .
- CThe integral is undefined if and .
- DThe integral is undefined if , and .
- EThe integral is undefined only if or .
Q18:
Is an improper integral?
- Ano
- Byes
Q19:
Is an improper integral?
- AYes
- BNo