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4.6 Integration (A-level only)

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Question 58

An industrial spill of a viscous lubricant is spreading across a flat floor. The area of the spill, $\text{ m}^2$ , at time $t$ hours after the spill is discovered, is modelled by the differential equation

\frac{dL}{dt} = \frac{L\sqrt{L}}{5t^2}, \quad t > 0

Given that the spill covers $\text{ m}^2$ at the moment it is discovered ( $t = 1$ ),

show that

\left( \frac{pt}{qt + r} \right)^2

where $p$ , $q$ , and $r$ are integers to be found.

[6]

According to the model, find the limiting value of the area covered by the spill as $\to \infty$ .

[2]

Markscheme

4.6 Integration (A-level only) Questions

A Level
Maths
4.6 Integration (A-level only)

92 exam-style questions on WJEC A Level Maths 4.6 Integration (A-level only), covering 4.6.1 Integration (A-level only) and 4.6.2 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

4.6 Integration (A-level only)

Question bank

4.6 Integration (A-level only)

Medium Hard

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Question 58

\frac{dL}{dt} = \frac{L\sqrt{L}}{5t^2}, \quad t > 0

Given that the spill covers $\text{ m}^2$ at the moment it is discovered ( $t = 1$ ),

show that

\left( \frac{pt}{qt + r} \right)^2

where $p$ , $q$ , and $r$ are integers to be found.

[6]

According to the model, find the limiting value of the area covered by the spill as $\to \infty$ .

[2]

Markscheme

4.6 Integration (A-level only) Questions

A Level
Maths
4.6 Integration (A-level only)