The volume of excess reagent, VVV (in litres), produced in a chemical reaction is modelled by the probability density function
f(v)={kv(25−v2)0≤v≤50otherwise f(v) = \begin{cases} kv(25 - v^2) & 0 \le v \le 5 \\ 0 & \text{otherwise} \end{cases} f(v)={kv(25−v2)00≤v≤5otherwiseShow that k=4625k = \frac{4}{625}k=6254.
Using integration, determine:
the mean volume of excess reagent produced per reaction,
the probability that a reaction produces more than 3 litres of excess reagent.
Three independent reactions are carried out.
Find the probability that at least 2 of these reactions produce more than 3 litres of excess reagent.
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.
