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1.11 H: Integration

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Question 30
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

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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