The rate of mass accumulation in a sediment trap is modeled by the function R(t)=12t4t+1R(t) = \dfrac{12t}{\sqrt{4t+1}}R(t)=4t+112t, where R R\,R is the rate in grams per day and t t\,t is the time in days since the start of the study. Using a suitable substitution, find the exact mass accumulated during the first 2 days.
Find ∫6x2−12x−26(x−4)(2x+3) dx\int \dfrac{6x^2 - 12x - 26}{(x - 4)(2x + 3)} \, dx∫(x−4)(2x+3)6x2−12x−26dx
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.
