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1.11 H: Integration

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Question 47

The rate of biomass accumulation in a soil sample, BBB (measured in mg per day), is modeled as a function of the nitrogen concentration nnn (in parts per million) by the equation:

B(n)=5n−3n2−n,n>1 B(n) = \frac{5n - 3}{n^2 - n}, \quad n > 1 B(n)=n2−n5n−3​,n>1
a.

Express B(n)B(n)B(n) in partial fractions.

[3]
b.

Hence find ∫B(n) dn\displaystyle \int B(n) \, dn∫B(n)dn.

[3]
c.

Use your answer to part (b) to find the value of kkk for which the total biomass accumulation between concentration levels n=kn = kn=k and n=2kn = 2kn=2k is exactly ln⁡72\ln 72ln72, where k>1k > 1k>1.

∫k2kB(n) dn=ln⁡72 \int_k^{2k} B(n) \, dn = \ln 72 ∫k2k​B(n)dn=ln72
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Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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