11.7 Partial Fractions

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A structural engineer models the rate of change of deflection $y\,$ of a loaded beam using the gradient function:

$dydx=7x+1(x−2)(2x+1)2,x>2\frac{dy}{dx} = \frac{7x+1}{(x-2)(2x+1)^2}, \quad x > 2$

Find the values of the constants $A$ , $B\,$ and $C\,$ such that

$7x+1(x−2)(2x+1)2≡Ax−2+B2x+1+C(2x+1)2\frac{7x+1}{(x-2)(2x+1)^2} \equiv \frac{A}{x-2} + \frac{B}{2x+1} + \frac{C}{(2x+1)^2}$

[4]

Hence find the exact change in deflection between $x = 3$ and $x = 4$ by calculating

$dx\int_{3}^{4} \frac{7x+1}{(x-2)(2x+1)^2} \, \mathrm{d}x$

giving your answer in the form $\ln q + r$ where $p$ , $q\,$ and $r\,$ are rational numbers.

[5]

11.7 Partial Fractions Questions

Practise Edexcel A Level Maths 11.7 Partial Fractions with exam-style questions for A Level Maths. 19 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.