A synthetic crystal's mass growth rate, dmdt\displaystyle \frac{dm}{dt}dtdm in grams per hour, is modeled by the equation:
dmdt=15t3−45t,t>0 \frac{dm}{dt} = \frac{15t^3 - 4}{5\sqrt{t}}, \quad t > 0 dtdm=5t15t3−4,t>0where t t\,t is the time elapsed in hours. Determine the general expression for the mass m m\,m in terms of ttt, giving your answer in its 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.
