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
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.
Find f(x)f(x)f(x).
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
