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3.6 Integration (A-level only)

3.6 Integration (A-level only)

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Question 258
a.

Use the substitution u=1+tu = 1 + \sqrt{t}u=1+t​ to show that the integral

∫12t1+t dt \int \frac{12\sqrt{t}}{1+\sqrt{t}} \, dt ∫1+t​12t​​dt

can be written in the form

∫(24u−48+24u) du \int \left( 24u - 48 + \frac{24}{u} \right) \, du ∫(24u−48+u24​)du
[4]
b.

The mass of a fungal colony, mmm grams, grows at a rate modelled by the equation

dmdt=12t1+t \frac{dm}{dt} = \frac{12\sqrt{t}}{1+\sqrt{t}} dtdm​=1+t​12t​​

where ttt is the number of days since the colony was first observed, for 1≤t≤91 \le t \le 91≤t≤9.

Determine the total increase in the mass of the colony from the end of day 1 to the end of day 9. Show each stage of your working and give your answer to one decimal place.

[4]
Markscheme

3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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