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1.11 H: Integration

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Question 109

The profile of a high-precision optical lens is modelled by a curve C C\,C with equation y=f(x)y = f(x)y=f(x) for x>0x > 0x>0.

Given that

  • f′(x)=8x2−(x−4)(2x+5)2xf'(x) = 8x^2 - \dfrac{(x - 4)(2x + 5)}{2\sqrt{x}}f′(x)=8x2−2x​(x−4)(2x+5)​
  • the point P(1,12)P(1, 12)P(1,12) lies on CCC
a.

find the equation of the normal to C C\,C at PPP, giving your answer in the form y=mx+cy = mx + cy=mx+c where m m\,m and c c\,c are constants to be found.

[4]
b.

find f(x)f(x)f(x), giving each term in simplest form.

[5]
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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