# Worksheet: Integration by Partial Fractions with Linear Factors

In this worksheet, we will practice using partial fractions to evaluate integrals of rational functions with linear factors.

Q1:

Use partial fractions to evaluate .

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• E

Q2:

Use partial fractions to evaluate .

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Q3:

Use partial fractions to evaluate .

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Q4:

Use partial fractions to evaluate .

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Q5:

Use partial fractions to find an analytic expression for the integral

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Q6:

Find so that and .

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

Q8:

Use partial fractions to evaluate .

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Q9:

Use partial fractions to evaluate .

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Q10:

Use partial fractions to evaluate .

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Q11:

Use partial fractions to evaluate .

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Q12:

Use partial fractions to evaluate the integral .

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Q13:

Use partial fractions to evaluate the integral .

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Q14:

Use partial fractions to evaluate the integral .

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Q15:

Use partial fractions to evaluate the integral .

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