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1.8 Integration

1.8 Integration

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Question 233
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

1.8 Integration Questions

  1. A Level
  2. /Maths
  3. /1.8 Integration

438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

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