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Question 231
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]

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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