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