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3.6 Integration (A-level only)

3.6 Integration (A-level only)

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Question 262

A gas flow system has a net rate of production R(t)R(t)R(t) given by R(t)=t4t+9R(t) = t\sqrt{4t+9}R(t)=t4t+9​ in m3h−1\text{m}^3\text{h}^{-1}m3h−1, where t t\,t is time in hours.

Use integration by substitution to show that the net volume of gas produced during the interval −2.25≤t≤4-2.25 \le t \le 4−2.25≤t≤4, given by

V=∫−2.254t4t+9 dt V = \int_{-2.25}^{4} t\sqrt{4t+9} \, dt V=∫−2.254​t4t+9​dt

is exactly 31.25 m3.

Fully justify your answer.

[5]
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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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