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11.6 Integration by Parts

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Question 31

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

\frac{8 + 2t^3 + \ln t}{t^4}, \quad t \ge 1

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

Find $dt\displaystyle \int \frac{\ln t}{t^4} \,\text{d}t$

[3]

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

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

[5]

Markscheme

11.6 Integration by Parts Questions

A Level
Maths
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.

11.6 Integration by Parts

Question bank

11.6 Integration by Parts

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

Question 31

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

\frac{8 + 2t^3 + \ln t}{t^4}, \quad t \ge 1

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

Find $dt\displaystyle \int \frac{\ln t}{t^4} \,\text{d}t$

[3]

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

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

[5]

Markscheme

11.6 Integration by Parts Questions

A Level
Maths
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.