2023TrialShort answer

Q13 (c) (i)

3 marks

Question

Find real numbers $a$ , $b$ and $c$ such that

\frac{10}{(x+1)(x^2+4)}\equiv\frac{a}{x+1}+\frac{bx+c}{x^2+4}.

Try the question before revealing the answer.

Solution

\frac{10}{(x+1)(x^2+4)}\equiv\frac{a}{x+1}+\frac{bx+c}{x^2+4}

\begin{aligned} 10&=a(x^2+4)+(bx+c)(x+1)\\ x=-1&\Rightarrow 10=5a\quad\therefore a=2\\ x=0&\Rightarrow 10=4a+c\quad\therefore c=2\\ x=1&\Rightarrow 10=5a+2(b+c)\quad\therefore b=-2\\ \therefore a&=2,\quad b=-2,\quad c=2 \end{aligned}

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Syllabus alignment

Calculus

Further IntegrationApply substitution, partial fractions, integration by parts and recurrence relationships to theoretical and practical problems.

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