Integration using Partial Fractions (AQA A-Level Mathematics): Quizzes

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Integration using Partial Fractions
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What is the main purpose of using partial fractions in integration?

To break rational functions into simpler fractions

What is the first step in the method for integration using partial fractions?

Factor the denominator

If a denominator contains x2+ax^2 + a, what form should the partial fraction component take?

Ax+Bx2+a\frac{Ax + B}{x^2 + a}

For 1(x+4)(x−4)=Ax+4+Bx−4\frac{1}{(x+4)(x-4)} = \frac{A}{x+4} + \frac{B}{x-4}, what is the value of BB when x=4x=4?

18\frac{1}{8}

What is the result of integrating ∫1x+4dx\int \frac{1}{x+4} dx?

ln⁡∣x+4∣+c\ln|x+4| + c

For 20(x+3)(x2+1)\frac{20}{(x+3)(x^2+1)}, what partial fraction form is used?

Ax+3+Bx+Cx2+1\frac{A}{x+3} + \frac{Bx+C}{x^2+1}

How many constants need to be found for Ax+3+Bx+Cx2+1\frac{A}{x+3} + \frac{Bx+C}{x^2+1}?

3

Which method involves comparing coefficients of like powers of xx?

Equating coefficients

What form does ∫9x2+3dx\int \frac{9}{x^2+3} dx integrate to?

93arctan⁡(x3)+c\frac{9}{\sqrt{3}}\arctan(\frac{x}{\sqrt{3}})+c

How can ln⁡∣x−4∣−ln⁡∣x+4∣\ln|x-4| - \ln|x+4| be simplified?

ln⁡∣x−4x+4∣\ln|\frac{x-4}{x+4}|

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