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.
363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.