Skip to content

Course home

Sign up

3.6 Integration (A-level only)

EasyMediumHard
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980818283848586878889909192939495
Question 73

An industrial spill of a viscous lubricant is spreading across a flat floor. The area of the spill, L m2L \text{ m}^2L m2, at time ttt hours after the spill is discovered, is modelled by the differential equation

dLdt=LL5t2,t>0 \frac{dL}{dt} = \frac{L\sqrt{L}}{5t^2}, \quad t > 0 dtdL​=5t2LL​​,t>0

Given that the spill covers 16 m216 \text{ m}^216 m2 at the moment it is discovered (t=1t = 1t=1),

a.

show that

L=(ptqt+r)2 L = \left( \frac{pt}{qt + r} \right)^2 L=(qt+rpt​)2

where ppp, qqq, and rrr are integers to be found.

[6]
b.

According to the model, find the limiting value of the area covered by the spill as t→∞t \to \inftyt→∞.

[2]
Markscheme

3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank