A scientist monitoring the growth of a synthetic crystal determines that the rate of change of its mass, MMM in milligrams, with respect to time ttt in hours, is given by:
dMdt=5t4−3t34,t>0 \frac{dM}{dt} = 5t^4 - \frac{3}{\sqrt[4]{t^3}}, \quad t > 0 dtdM=5t4−4t33,t>0Determine the general expression for the mass M(t)M(t)M(t).
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.
