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1.11 H: Integration

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Question 143

A curve C C\,C has equation y=f(x)y = f(x)y=f(x), x>0x > 0x>0.

Given that

  • f′′(x)=6x−1x2f''(x) = 6x - \dfrac{1}{x^2}f′′(x)=6x−x21​
  • the point P P\,P has xxx-coordinate 1 and lies on CCC
  • the tangent to C C\,C at P P\,P has equation y=5x−3y = 5x - 3y=5x−3
a.

Find an equation of the normal to C C\,C at PPP.

[4]
b.

Find f(x)f(x)f(x), writing your answer in simplest form.

[6]
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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