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.
363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.