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>2.5R(t) = \frac{10t - 15}{2t^2 - 5t}, \quad t > 2.5R(t)=2t2−5t10t−15,t>2.5
where 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=ln72
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.