# 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
• B
• C
• D
• E0

Q2:

Determine whether the integral is convergent or divergent.

• BConvergent

Q3:

Determine whether the integral is convergent or divergent.

• Aconvergent
• Bdivergent

Q4:

The integral is convergent. What does it converge to?

• A
• B
• C0
• 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.

• Aconvergent
• Bdivergent

Q8:

The integral is convergent. What does it converge to?

• A
• B
• C
• D
• E

Q9:

Determine whether the integral is convergent or divergent.

• Bconvergent

Q10:

The integral is convergent. What does it converge to?

Q11:

Determine whether the integral is convergent or divergent.

• Bconvergent

Q12:

Determine whether the integral is convergent or divergent.

• Aconvergent
• Bdivergent

Q13:

Determine whether the integral is convergent or divergent.

• Bconvergent

Q14:

The integral is convergent. What does it converge to?

• A
• B
• C
• D
• E2

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 undefined if , and .
• CThe integral is defined for all finite values of and .
• DThe integral is undefined only if or .
• EThe integral is undefined if and .

Q18:

Is an improper integral?

• Ayes
• Bno

Q19:

Is an improper integral?

• AYes
• BNo