Find, in simplest form,
∫3(2x−5)4 dx \int \frac{3}{(2x - 5)^4} \, \mathrm{d}x ∫(2x−5)43dxA population of bacteria grows at a rate R(t)=82t+1\displaystyle R(t) = \frac{8}{2t + 1}R(t)=2t+18 million per hour, where t t\,t is the time in hours, t≥0t \ge 0t≥0.
Show, by algebraic integration, that the total growth in the population between t=1t = 1t=1 and t=3t = 3t=3 is lnb \ln b\,lnb million, where b b\,b is a rational constant to be found.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
