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 > 0dtdm=5t15t3−4,t>0
where 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 Edexcel A Level Maths 11.1 Integrating Standard Functions with exam-style questions for A Level Maths. 81 questions, matched to the Edexcel A Level Maths (9MA0) 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.