The rate of mass accumulation of a certain chemical product in a reaction, RRR in grams per minute, is modeled by the function
R(t)=10t−152t2−5t,t>2.5 R(t) = \frac{10t - 15}{2t^2 - 5t}, \quad t > 2.5 R(t)=2t2−5t10t−15,t>2.5where ttt is the time in minutes since the reaction began.
Express R(t)R(t)R(t) in partial fractions.
Hence find ∫R(t) dt\int R(t) \, dt∫R(t)dt.
Use your answer to part (b) to find the value of the constant kkk for which
∫k2kR(t) dt=ln72 \int_k^{2k} R(t) \, dt = \ln 72 ∫k2kR(t)dt=ln72Practise 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.
