The rate at which a chemical residue accumulates in a filtration system, R R\,R milligrams per hour, is modeled by the equation:
R(t)=(5t−2)(3t+1)3t,t>0 R(t) = \frac{(5\sqrt{t} - 2)(3t + 1)}{3\sqrt{t}}, \quad t > 0 R(t)=3t(5t−2)(3t+1),t>0where t t\,t is the time in hours since the filter was installed. Determine the general expression for the total mass of residue, M(t)M(t)M(t), in the system, giving your answer in simplest form.
Practise 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.
