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.
864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.