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1.11 H: Integration

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Question 172

The profile of a cooling fin in a high-performance engine is modeled by a curve CCC in the (x,y)(x, y)(x,y) plane. For y>0y > 0y>0, the gradient of the curve at any point (x,y)(x, y)(x,y) is given by the differential equation

dydx=x3y227 \frac{dy}{dx} = \frac{x^3 y^2}{27} dxdy​=27x3y2​

The curve CCC passes through the point with coordinates (3,1)(3, 1)(3,1). Show that CCC intersects the coordinate axes at exactly one point and state the coordinates of this point. Fully justify your answer.

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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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