The curve C C\,C has equation
y=184(2x−k),x≠k2 y = \frac{18}{4(2x - k)}, \quad x \neq \frac{k}{2} y=4(2x−k)18,x=2kwhere k k\,k is a positive constant and k≠2k \neq 2k=2.
Find dydx\displaystyle \frac{dy}{dx}dxdy giving your answer in simplest form in terms of kkk.
The point P P\,P with x x\,x coordinate 1 lies on CCC. Given that the gradient of the curve at P P\,P is -9, find the two possible values of kkk.
Given also that k<2k < 2k<2, find the equation of the normal to C C\,C at PPP, writing your answer in the form ax+by+c=0ax + by + c = 0ax+by+c=0, where a,b a, b\,a,b and c c\,c are integers to be found.
Show, using algebraic integration, that
∫13184(2x−k) dx=λln(5) \int_{1}^{3} \frac{18}{4(2x - k)} \, dx = \lambda \ln(5) ∫134(2x−k)18dx=λln(5)where λ \lambda\,λ is a constant to be found.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, 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.
