A prototype high-pressure vessel's volume V V\,V changes with respect to the internal pressure ppp (where p>0p > 0p>0) according to the rate:
dVdp=8p3−3p2p2\frac{dV}{dp} = \frac{8p^3 - 3\sqrt{p}}{2p^2}dpdV=2p28p3−3p
Determine the general expression for V V\,V in terms of ppp, 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.