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1.11 H: Integration

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Question 74

The rate of change of the volume of water, VVV, being pumped into a reservoir is modeled by the equation

dVdt=7t24−52t4+23 \frac{dV}{dt} = \frac{7t^2}{4} - \frac{5}{2t^4} + \frac{2}{3} dtdV​=47t2​−2t45​+32​

where VVV is measured in cubic metres and ttt is the time in hours since pumping began. Determine the general expression for VVV in terms of ttt, giving each term 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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