The rate of growth of a specific bacteria population in a petri dish, G(t)G(t)G(t) in thousands of bacteria per hour, is modeled by the function
G(t)=122+2t+4 G(t) = \frac{12}{2 + \sqrt{2t + 4}} G(t)=2+2t+412for 0≤t≤160 \le t \le 160≤t≤16, where t t\,t is the time in hours since the start of the experiment. Using the substitution u=2+2t+4u = 2 + \sqrt{2t + 4}u=2+2t+4, find the exact total increase in the population over the 16-hour period by calculating the value of
∫016122+2t+4 dt \int_{0}^{16} \frac{12}{2 + \sqrt{2t + 4}} \, dt ∫0162+2t+412dtGive your answer in the form a+blnca + b \ln ca+blnc, where a,b, a, b,\,a,b, and c c\,c are integers.
864 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.