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=2p28p3−3pDetermine the general expression for V V\,V in terms of ppp, giving your answer in its simplest form.
438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.