1.8.9 Integration by parts (A-level only)

Question 8

A model for the power output $P$ (in megawatts) of a tidal turbine over an 11-hour cycle is given by

t^2) \ln t, \quad 1 \le t \le 9

where $t\,$ 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 $t = 1$ and $t = 9$ can be expressed in the form

\ln 3

where $p\,$ and $q\,$ are rational numbers to be determined.

[9]

1.8.9 Integration by parts (A-level only)

1 2 3 4 5 6 7 8

Question 8

A model for the power output $P$ (in megawatts) of a tidal turbine over an 11-hour cycle is given by

t^2) \ln t, \quad 1 \le t \le 9

where $t\,$ 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 $t = 1$ and $t = 9$ can be expressed in the form

\ln 3

where $p\,$ and $q\,$ are rational numbers to be determined.

[9]

1.8.9 Integration by parts (A-level only)

Question 8

1.8.9 Integration by parts (A-level only) Questions

1.8.9 Integration by parts (A-level only)

Question 8

1.8.9 Integration by parts (A-level only) Questions