The concentration CCC of a specific pheromone within a beehive varies with the distance xxx (measured in metres) from the entrance according to a complex biological model.
Express 5(1+4x)(1−x)\frac{5}{(1+4x)(1-x)}(1+4x)(1−x)5 in partial fractions.
The relationship between the concentration and the distance is governed by the differential equation
(1+4x)(1−x)dCdx=tanC (1+4x)(1-x) \frac{dC}{dx} = \tan C (1+4x)(1−x)dxdC=tanCfor the interval −14<x<1-\frac{1}{4} < x < 1−41<x<1. Given that the concentration at the entrance is C=π2C = \frac{\pi}{2}C=2π when x=0x = 0x=0, determine the particular solution for this model.
Give your answer in the form sinnC=f(x)\sin^n C = f(x)sinnC=f(x), where nnn is an integer 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.
