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Question 546

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.

[4]
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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