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1.11.2 Integrating standard functions

1.11.2 Integrating standard functions

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Question 58
i.

Find, using algebraic integration, the exact value of

∫16102x+3dx \int_{1}^{6} \frac{10}{2x + 3} dx ∫16​2x+310​dx

giving your answer in simplest form.

[3]
ii.

The rate of oxygen consumption in a bioreactor, G(t)G(t)G(t), is modeled by the function G(t)=2t3−7t2−12t+52(t−3)2G(t) = \frac{2t^3 - 7t^2 - 12t + 52}{(t - 3)^2}G(t)=(t−3)22t3−7t2−12t+52​ for t>3t > 3t>3.

Given that G(t)=At+B+C(t−3)2G(t) = At + B + \frac{C}{(t - 3)^2}G(t)=At+B+(t−3)2C​ where AAA, BBB and CCC are constants to be found, find

∫G(t)dt \int G(t) dt ∫G(t)dt
[5]
Markscheme

1.11.2 Integrating standard functions Questions

  1. A Level
  2. /Maths
  3. /1.11.2 Integrating standard functions

139 exam-style questions on AQA A Level Maths 1.11.2 Integrating standard functions. Each one has a worked solution and a mark scheme showing where the marks go.

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