1.8.9 Integration by parts (A-level only)

A robotic arm's angular velocity $ω\omega$ (in rad s $^{-1}$ ) over the interval $\le t \le \pi$ is modelled by the function

\omega(t) = t \cos\left(\frac{1}{2}t\right)

where $t$ is the time in seconds.

Show that the total angular displacement of the arm between $t = 0$ and $\pi$ is $(2π−4)(2\pi - 4)$ radians.

[5]

A robotic arm's angular velocity $ω\omega$ (in rad s $^{-1}$ ) over the interval $\le t \le \pi$ is modelled by the function

\omega(t) = t \cos\left(\frac{1}{2}t\right)

where $t$ is the time in seconds.

Show that the total angular displacement of the arm between $t = 0$ and $\pi$ is $(2π−4)(2\pi - 4)$ radians.

[5]

1.8.9 Integration by parts (A-level only) Questions