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1.11 H: Integration

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Question 168
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

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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