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1.11 H: Integration

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Question 136

A beam of light travels through a container of murky liquid. The rate of change of the light's intensity, III lux, with respect to the depth, xxx metres, is modeled by the equation:

R=−0.75I2 R = -0.75 I^2 R=−0.75I2

where RRR is the rate of change dIdx\frac{dI}{dx}dxdI​. The intensity of the light as it enters the liquid at the surface (where x=0x = 0x=0) is 444 lux.

a.

By first forming a suitable differential equation, show that

I=43x+1 I = \frac{4}{3x + 1} I=3x+14​
[4]
b.

Determine the rate of change of the light's intensity with respect to depth when x=1x = 1x=1.

[2]
Markscheme

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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