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Question 649

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+1​20​, 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 ∫012​3+2t+1​20​dt

Using 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+bln⁡ca + b \ln ca+blnc, where aaa, bbb, and ccc are integers.

[6]
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Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

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.

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