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≤9 P(t) = (9t - t^2) \ln t, \quad 1 \le t \le 9 P(t)=(9t−t2)lnt,1≤t≤9where 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+qln3 p + q \ln 3 p+qln3where p p\,p and q q\,q are rational numbers to be determined.
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.
