# Worksheet: Integration by Partial Fractions with repeated Linear Factors

Q1:

Use partial fractions to evaluate .

• A
• B
• C
• D
• E

Q2:

Use partial fractions to evaluate .

• A
• B
• C
• D
• E

Q3:

Use partial fractions to evaluate .

• A
• B
• C
• D
• E

Q4:

Use partial fractions to evaluate .

• A
• B
• C
• D
• E

Q5:

Use partial fractions to find an analytic expression for the integral

• A
• B
• C
• D
• E

Q6:

Find so that and .

• A
• B
• C
• D
• E

Q7:

Consider the function which is defined on .

Find an antiderivative of such that . What is ?

• A.
• B.
• C.
• D.
• E.

Is it possible to find an antiderivative that satisfies , where ? If so, what is ?

• AYes,
• Bno

What you have found above seems to violate the result that says that any two antiderivatives must differ by a constant function, because is not a constant function. Why is there no contradiction?

• Abecause that result only holds sometimes; sometimes it fails
• Bbecause is constant; it has the value 0 on and the value 1 on
• Cbecause that result assumes that the domain is an interval
• Dbecause that result requires additional conditions to the antiderivatives
• Ebecause neither nor is differentiable; that result only applies to differentiable functions