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Question 598

The curve C with equation y=f(x)y = f(x)y=f(x), x>0x > 0x>0, passes through the point P(9,2)P(9, 2)P(9,2).

Given that f′(x)=2x−5+18x2f'(x) = 2\sqrt{x} - 5 + \frac{18}{x^2}f′(x)=2x​−5+x218​

a.

find the equation of the normal to C at P. Write your answer in the form ax+by+c=0ax + by + c = 0ax+by+c=0, where aaa, bbb and ccc are integers to be found.

[4]
b.

Find f(x)f(x)f(x).

[4]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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