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1.8 Integration

1.8 Integration

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Question 331

The altitude H H\,H of a research drone, measured in kilometres, is modelled by the curve C C\,C with equation H=f(t)H = f(t)H=f(t) for t>0t > 0t>0, where t t\,t is the time in hours since it reached a specific tracking station.

Given that

  • f′(t)=4t−(t−4)(3t+2)4tf'(t) = 4t - \dfrac{(t - 4)(3t + 2)}{4\sqrt{t}}f′(t)=4t−4t​(t−4)(3t+2)​
  • the point P(4,10)P(4, 10)P(4,10) lies on CCC
a.

find the equation of the normal to C C\,C at PPP, giving your answer in the form H=mt+cH = mt + cH=mt+c where m m\,m and c c\,c are constants to be found.

[4]
b.

find f(t)f(t)f(t), giving each term in simplest form.

[6]
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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