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 AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
