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3.6 Integration (A-level only)

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Question 27
a.

Given that y=1y = 1y=1 at x=0x = 0x=0, solve the differential equation

dydx=12xy12e3x,y≥0 \frac{\text{d}y}{\text{d}x} = \frac{12xy^{\frac{1}{2}}}{\text{e}^{3x}}, \quad y \ge 0 dxdy​=e3x12xy21​​,y≥0

giving your answer in the form y12=g(x)y^{\frac{1}{2}} = g(x)y21​=g(x).

[6]
b.

Hence find the equation of the horizontal asymptote to the curve with equation y12=g(x)y^{\frac{1}{2}} = g(x)y21​=g(x).

[3]
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.

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