Skip to content

Course home

3.6 Integration (A-level only)

3.6 Integration (A-level only)

EasyMediumHard
12345678910111213141516171819202122232425262728293031323334353637383940414243444546
Question 40

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

3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

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.

Question bank