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Question 652

The duration, T T\,T in hours, of a specific industrial chemical reaction is modeled by the probability density function

f(t)={kt(16−t2)0≤t≤40otherwise f(t) = \begin{cases} kt(16 - t^2) & 0 \le t \le 4 \\ 0 & \text{otherwise} \end{cases} f(t)={kt(16−t2)0​0≤t≤4otherwise​
a.

Show that k=164\displaystyle k = \frac{1}{64}k=641​.

[3]
b.

Using integration, find

the mean duration of the reaction,

[3]
c.

the probability that a reaction lasts for more than 3 hours.

[3]
d.

Three independent reactions are monitored.

Determine the probability that at least 2 of the reactions last for more than 3 hours.

[3]
Markscheme

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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