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Question 545

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.

[3]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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