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Question 143

A model for the power output PPP (in megawatts) of a tidal turbine over an 11-hour cycle is given by

P(t)=(9t−t2)ln⁡t,1≤t≤9 P(t) = (9t - t^2) \ln t, \quad 1 \le t \le 9 P(t)=(9t−t2)lnt,1≤t≤9

where t t\,t is the time in hours after the start of the observation period. The total energy generated during this period is given by the area under the power-time graph.

Show that the total energy generated between t=1t = 1t=1 and t=9t = 9t=9 can be expressed in the form

p+qln⁡3 p + q \ln 3 p+qln3

where p p\,p and q q\,q are rational numbers to be determined.

[9]
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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