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)lnt,1≤t≤9P(t) = (9t - t^2) \ln t, \quad 1 \le t \le 9P(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+qln3p + q \ln 3p+qln3 where p p\,p and q q\,q are rational numbers to be determined.
Practise Edexcel A Level Maths 11.6 Integration by Parts with exam-style questions for A Level Maths. 52 questions, 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.