11.2 Integrating f(ax + b)

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The curve $C\,$ has equation

$\frac{18}{4(2x - k)}, \quad x \neq \frac{k}{2}$

where $k\,$ is a positive constant and $\neq 2$ .

Find $dydx\displaystyle \frac{dy}{dx}$ giving your answer in simplest form in terms of $k$ .

[2]

The point $P\,$ with $x\,$ coordinate 1 lies on $C$ . Given that the gradient of the curve at $P\,$ is -9, find the two possible values of $k$ .

[3]

Given also that $k < 2$ , find the equation of the normal to $C\,$ at $P$ , writing your answer in the form $a x + b y + c = 0$ , where $b\,$ and $c\,$ are integers to be found.

[3]

Show, using algebraic integration, that

$dx=λln⁡(5)\int_{1}^{3} \frac{18}{4(2x - k)} \, dx = \lambda \ln(5)$

where $\lambda\,$ is a constant to be found.

[3]

11.2 Integrating f(ax + b) Questions

Practise Edexcel A Level Maths 11.2 Integrating f(ax + b) with exam-style questions for A Level Maths. 28 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.