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1.8.9 Integration by parts (A-level only)

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Question 25

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

The velocity v(t)v(t)v(t), in mm s−1\text{mm s}^{-1}mm s−1, of a microscopic probe is modeled by the function

v(t)=12tcos⁡(3t),0≤t≤π6 v(t) = 12t \cos(3t), \quad 0 \le t \le \frac{\pi}{6} v(t)=12tcos(3t),0≤t≤6π​

where t t\,t is the time in seconds since the measurement began.

Find the total displacement of the probe over the interval 0≤t≤π6\displaystyle 0 \le t \le \frac{\pi}{6}0≤t≤6π​, giving your answer in simplest form.

[5]
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1.8.9 Integration by parts (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.8.9 Integration by parts (A-level only)

52 exam-style questions on OCR A Level Maths 1.8.9 Integration by parts (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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