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1.11 H: Integration

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Question 73

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.

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Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, 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). Each one has a worked solution and a mark scheme showing where the marks go.

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