Skip to content

Course home

Sign up

11.6 Integration by Parts

EasyMediumHard
123456789101112131415161718192021222324252627
Question 17

A geologist models the rate of thermal energy emission, PPP, from a cooling volcanic vent using the equation

P(t)=8+2t3+ln⁡tt4,t≥1 P(t) = \frac{8 + 2t^3 + \ln t}{t^4}, \quad t \ge 1 P(t)=t48+2t3+lnt​,t≥1

where P P\,P is measured in megawatts and t t\,t is the time in hours since initial observation.

a.

Find ∫ln⁡tt4 dt\displaystyle \int \frac{\ln t}{t^4} \,\text{d}t∫t4lnt​dt

[3]
b.

The total energy EEE, in megawatt-hours, emitted by the vent between t=1t = 1t=1 and t=2t = 2t=2 is given by the area under the curve P(t)P(t)P(t) between these two times.

Use your result from part (a) to calculate the exact value of EEE. Give your answer in the form a+ln⁡ba + \ln ba+lnb, where a a\,a and b b\,b are constants to be determined.

[5]
Markscheme

11.6 Integration by Parts Questions

  1. A Level
  2. /Maths
  3. /11.6 Integration by Parts

52 exam-style questions on Edexcel A Level Maths 11.6 Integration by Parts. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank