A laboratory technician models the rate of change of the volume, VVV, of a liquid in a cooling system. The model used is
dVdt=5t2+46t3,t>0 \frac{dV}{dt} = \frac{5t^2 + 4}{6t^3}, \quad t > 0 dtdV=6t35t2+4,t>0where ttt is the time in hours. Determine the general expression for VVV in terms of ttt, 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.
