1.11.5 Integration by substitution and by parts (A-level only)

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

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

\cos(3t), \quad 0 \le t \le \frac{\pi}{6}

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

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

[5]

1.11.5 Integration by substitution and by parts (A-level only) Questions

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

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

\cos(3t), \quad 0 \le t \le \frac{\pi}{6}

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

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

[5]