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Question 589
i.

Find

∫(4−3x)25x dx,x>0 \int \frac{(4-3x)^2}{5\sqrt{x}} \, dx, \quad x > 0 ∫5x​(4−3x)2​dx,x>0

giving your answer in simplest form.

[4]
ii.

The rate of change of the depth of water, DDD metres, in a reservoir with respect to time ttt days is modeled by the equation dDdt=t2+at+b\frac{dD}{dt} = t^2 + at + bdtdD​=t2+at+b for 0≤t≤100 \le t \le 100≤t≤10, where aaa and bbb are constants.

  • At the start of a monitoring period (t=0t = 0t=0), the depth is 15 metres.
  • After 3 days, the depth has fallen to 9 metres.
  • On the 3rd day (t=3t = 3t=3), the depth is decreasing at a rate of 2 metres per day.

Determine the expression for DDD in terms of ttt, giving your answer in simplest form.

[7]
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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