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1 Pure Mathematics

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Question 108

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.

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1 Pure Mathematics Questions

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1.1.3 Set theory language and symbols
1.1.4 Definition, domain and range of functions