The concentration of a certain chemical reagent, CCC, measured in mmol/L, during a reaction is modelled by the equation
C(t)=3+4log10(cost)for 0≤t≤1 C(t) = 3 + 4 \log_{10}(\cos t) \quad \text{for } 0 \le t \le 1 C(t)=3+4log10(cost)for 0≤t≤1where ttt is the time in seconds after the reaction begins.
Complete the table below for the concentration at various times, giving values of CCC to 3 decimal places.
| ttt | 0 | 0.25 | 0.5 | 0.75 | 1 |
|---|---|---|---|---|---|
| CCC | 3.000 | 2.773 | 1.931 |
Use the trapezium rule with all the values in the completed table to find an estimate for ∫01C(t) dt\int_{0}^{1} C(t) \, dt∫01C(t)dt, giving your answer to 2 decimal places.
Hence, determine an estimate for the value of
∫01(1−2log10(cost)) dt \int_{0}^{1} (1 - 2 \log_{10}(\cos t)) \, dt ∫01(1−2log10(cost))dtgiving your answer to 2 decimal places.
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.
