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Question 582
i.

Find

∫2x2e−4x dx \int 2x^2 e^{-4x} \, dx ∫2x2e−4xdx

writing the answer in simplest form.

[4]
ii.

The rate of change of the volume of water in a reservoir, VVV (in megalitres per hour), is modeled by the equation

dVdt=10t+2(t−1)(2t+1),t>1 \frac{dV}{dt} = \frac{10t+2}{(t-1)(2t+1)}, \quad t > 1 dtdV​=(t−1)(2t+1)10t+2​,t>1

where t t\,t is the time in hours since a valve was opened. Use partial fractions and algebraic integration to show that the total change in volume between t=2t = 2t=2 and t=4t = 4t=4 is ln⁡k \ln k\,lnk megalitres, where k k\,k is a fully simplified rational constant to be found.

[6]
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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