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3.6 Integration (A-level only)

3.6 Integration (A-level only)

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Question 19

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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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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