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>1Express B(n)B(n)B(n) in partial fractions.
Hence find ∫B(n) dn\displaystyle \int B(n) \, dn∫B(n)dn.
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 ln72\ln 72ln72, where k>1k > 1k>1.
∫k2kB(n) dn=ln72 \int_k^{2k} B(n) \, dn = \ln 72 ∫k2kB(n)dn=ln72864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.