In a chemical reactor, the rate of accumulation of a byproduct, MMM grams per hour, is given by the function R(t)=203+2t+1R(t) = \frac{20}{3 + \sqrt{2t + 1}}R(t)=3+2t+120, where ttt is the time in hours since the reaction started. The total mass produced between t=0t = 0t=0 and t=12t = 12t=12 is given by
∫012203+2t+1 dt \int_{0}^{12} \frac{20}{3 + \sqrt{2t + 1}} \, dt ∫0123+2t+120dtUsing the substitution u=3+2t+1u = 3 + \sqrt{2t + 1}u=3+2t+1, find the exact mass produced, giving your answer in the form a+blnca + b \ln ca+blnc, where aaa, bbb, and ccc are integers.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, matched to the Edexcel A Level Maths (9MA0) 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.
